Difference between revisions of "The Degree Diameter Problem for Circulant Graphs"
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(→Table of the orders of the largest known circulant graphs) |
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{| border="1" cellspacing="2" cellpadding="2" style="text-align: center;" | {| border="1" cellspacing="2" cellpadding="2" style="text-align: center;" | ||
− | | '''<math>d</math>\<math>k</math>'''|| '''2''' || '''3''' || '''4'''|| '''5''' || '''6''' || '''7''' || '''8''' || '''9''' || '''10''' || '''11''' || '''12''' | + | | '''<math>d</math>\<math>k</math>'''|| '''2''' || '''3''' || '''4'''|| '''5''' || '''6''' || '''7''' || '''8''' || '''9''' || '''10''' || '''11''' || '''12''' || '''13''' || '''14''' || '''15''' || '''16''' |
|- | |- | ||
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|- | |- | ||
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|- | |- | ||
− | | '''7''' ||style="background-color: magenta;" | '''26''' ||style="background-color: magenta;" | '''76''' ||style="background-color: magenta;" | '''160''' ||style="background-color: magenta;" | '''308''' ||style="background-color: magenta;" | '''536''' ||style="background-color: magenta;" | '''828''' ||style="background-color: magenta;" | '''1 232''' ||style="background-color: magenta;" | '''1 764''' ||style="background-color: magenta;" | '''2 392''' ||style="background-color: magenta;" | 3 180 ||style="background-color: magenta;" | 4 144 | + | | '''7''' ||style="background-color: magenta;" | '''26''' ||style="background-color: magenta;" | '''76''' ||style="background-color: magenta;" | '''160''' ||style="background-color: magenta;" | '''308''' ||style="background-color: magenta;" | '''536''' ||style="background-color: magenta;" | '''828''' ||style="background-color: magenta;" | '''1 232''' ||style="background-color: magenta;" | '''1 764''' ||style="background-color: magenta;" | '''2 392''' ||style="background-color: magenta;" | 3 180 ||style="background-color: magenta;" | 4 144 ||style="background-color: magenta;" | 5 236 ||style="background-color: magenta;" | 6 536 ||style="background-color: magenta;" | 8 060 ||style="background-color: magenta;" | 9 744 |
|- | |- | ||
− | | '''8''' ||style="background-color: #81BEF7;" | '''35''' ||style="background-color: #CCFF00;" | '''104''' ||style="background-color: #CCFF00;" | '''248''' ||style="background-color: #CCFF00;" | '''528''' ||style="background-color: #66ff66;" | '''984''' ||style="background-color: #66ff66;" | '''1 712''' ||style="background-color: #66ff66;" | 2 768 ||style="background-color: #66ff66;" | 4 280 ||style="background-color: #66ff66;" | 6 320 ||style="background-color: #66ff66;" | 9 048 ||style="background-color: #66ff66;" | 12 552 | + | | '''8''' ||style="background-color: #81BEF7;" | '''35''' ||style="background-color: #CCFF00;" | '''104''' ||style="background-color: #CCFF00;" | '''248''' ||style="background-color: #CCFF00;" | '''528''' ||style="background-color: #66ff66;" | '''984''' ||style="background-color: #66ff66;" | '''1 712''' ||style="background-color: #66ff66;" | 2 768 ||style="background-color: #66ff66;" | 4 280 ||style="background-color: #66ff66;" | 6 320 ||style="background-color: #66ff66;" | 9 048 ||style="background-color: #66ff66;" | 12 552 ||style="background-color: #66ff66;" | 17 024 ||style="background-color: #66ff66;" | 22 568 ||style="background-color: #66ff66;" | 29 408 ||style="background-color: #66ff66;" | 37 664 |
|- | |- | ||
− | | '''9''' ||style="background-color: #81BEF7;" | '''42''' || style="background-color: #66cc66;" | '''130''' ||style="background-color: #CCFF00;" | '''320''' ||style="background-color: #66ff66;" | '''700''' ||style="background-color: #66ff66;" | '''1 416''' ||style="background-color: #66ff66;" | 2 548 ||style="background-color: #66ff66;" | 4 304 ||style="background-color: #66ff66;" | 6 804 ||style="background-color: #66ff66;" | 10 320 ||style="background-color: #66ff66;" | 15 004 ||style="background-color: #66ff66;" | 21 192 | + | | '''9''' ||style="background-color: #81BEF7;" | '''42''' || style="background-color: #66cc66;" | '''130''' ||style="background-color: #CCFF00;" | '''320''' ||style="background-color: #66ff66;" | '''700''' ||style="background-color: #66ff66;" | '''1 416''' ||style="background-color: #66ff66;" | 2 548 ||style="background-color: #66ff66;" | 4 304 ||style="background-color: #66ff66;" | 6 804 ||style="background-color: #66ff66;" | 10 320 ||style="background-color: #66ff66;" | 15 004 ||style="background-color: #66ff66;" | 21 192 ||style="background-color: #66ff66;" | 29 068 ||style="background-color: #66ff66;" | 39 032 ||style="background-color: #66ff66;" | 51 300 ||style="background-color: #66ff66;" | 66 336 |
|- | |- | ||
− | | '''10''' ||style="background-color: #81BEF7;" | '''51''' || style="background-color: #66cc66;" | '''177''' ||style="background-color: yellow;" | '''457''' ||style="background-color: #66ff66;" | '''1 099''' ||style="background-color: orange;" | 2 380 ||style="background-color: orange;" | 4 551 ||style="background-color: orange;" | 8 288 ||style="background-color: orange;" | 14 099 ||style="background-color: orange;" | 22 805 ||style="background-color: #66ff66;" | 35 568 ||style="background-color: #66ff66;" | 53 025 | + | | '''10''' ||style="background-color: #81BEF7;" | '''51''' || style="background-color: #66cc66;" | '''177''' ||style="background-color: yellow;" | '''457''' ||style="background-color: #66ff66;" | '''1 099''' ||style="background-color: orange;" | 2 380 ||style="background-color: orange;" | 4 551 ||style="background-color: orange;" | 8 288 ||style="background-color: orange;" | 14 099 ||style="background-color: orange;" | 22 805 ||style="background-color: #66ff66;" | 35 568 ||style="background-color: #66ff66;" | 53 025 ||style="background-color: #66ff66;" | 77 572 ||style="background-color: #66ff66;" | 110 045 ||style="background-color: #66ff66;" | 152 671 ||style="background-color: #66ff66;" | 208 052 |
|- | |- | ||
− | | '''11''' ||style="background-color: #81BEF7;" | '''56''' ||style="background-color: yellow;" | '''210''' || style="background-color: yellow;" | '''576''' ||style="background-color: orange;" | 1 428 ||style="background-color: orange;" | 3 200 ||style="background-color: orange;" | 6 652 ||style="background-color: orange;" | 12 416 || style="background-color: orange;" | 21 572 ||style="background-color: orange;" | 35 880 ||style="background-color: #66ff66;" | 56 700 ||style="background-color: #66ff66;" | 87 248 | + | | '''11''' ||style="background-color: #81BEF7;" | '''56''' ||style="background-color: yellow;" | '''210''' || style="background-color: yellow;" | '''576''' ||style="background-color: orange;" | 1 428 ||style="background-color: orange;" | 3 200 ||style="background-color: orange;" | 6 652 ||style="background-color: orange;" | 12 416 || style="background-color: orange;" | 21 572 ||style="background-color: orange;" | 35 880 ||style="background-color: #66ff66;" | 56 700 ||style="background-color: #66ff66;" | 87 248 || style="background-color: #66ff66;" | 128 852 ||style="background-color: #66ff66;" | 184 424 ||style="background-color: #66ff66;" | 259 260 ||style="background-color: #66ff66;" | 355 576 |
|- | |- | ||
− | | '''12''' ||style="background-color: #81BEF7;" | '''67''' ||style="background-color: yellow;" | '''275''' ||style="background-color: orange;" | 819 ||style="background-color: #66ff66;" | 2 120 ||style="background-color: #66ff66;" | 5 044 ||style="background-color: #66ff66;" | 10 777 ||style="background-color: #66ff66;" | 21 384 ||style="background-color: #66ff66;" | 39 996 ||style="background-color: #66ff66;" | 69 965 ||style="background-color: #66ff66;" | 117 712 ||style="background-color: #66ff66;" | 190 392 | + | | '''12''' ||style="background-color: #81BEF7;" | '''67''' ||style="background-color: yellow;" | '''275''' ||style="background-color: orange;" | 819 ||style="background-color: #66ff66;" | 2 120 ||style="background-color: #66ff66;" | 5 044 ||style="background-color: #66ff66;" | 10 777 ||style="background-color: #66ff66;" | 21 384 ||style="background-color: #66ff66;" | 39 996 ||style="background-color: #66ff66;" | 69 965 ||style="background-color: #66ff66;" | 117 712 ||style="background-color: #66ff66;" | 190 392 ||style="background-color: #66ff66;" | 295 840 ||style="background-color: #66ff66;" | 448 920 ||style="background-color: #66ff66;" | 662 680 ||style="background-color: #66ff66;" | 952 985 |
|- | |- | ||
− | | '''13''' ||style="background-color: #81BEF7;" | '''80''' ||style="background-color: yellow;" | '''312''' ||style="background-color: orange;" | 970 ||style="background-color: #66ff66;" | 2 676 ||style="background-color: #66ff66;" | 6 256 ||style="background-color: #66ff66;" | 14 740 ||style="background-color: #66ff66;" | 30 760 ||style="background-color: #66ff66;" | 57 396 ||style="background-color: #66ff66;" | 106 120 ||style="background-color: #66ff66;" | 182 980 ||style="background-color: #66ff66;" | 295 840 | + | | '''13''' ||style="background-color: #81BEF7;" | '''80''' ||style="background-color: yellow;" | '''312''' ||style="background-color: orange;" | 970 ||style="background-color: #66ff66;" | 2 676 ||style="background-color: #66ff66;" | 6 256 ||style="background-color: #66ff66;" | 14 740 ||style="background-color: #66ff66;" | 30 760 ||style="background-color: #66ff66;" | 57 396 ||style="background-color: #66ff66;" | 106 120 ||style="background-color: #66ff66;" | 182 980 ||style="background-color: #66ff66;" | 295 840 ||style="background-color: #66ff66;" | 476 100 ||style="background-color: #66ff66;" | 732 744 ||style="background-color: #66ff66;" | 1 081 860 ||style="background-color: #66ff66;" | 1 593 064 |
|- | |- | ||
− | | '''14''' ||style="background-color: #81BEF7;" | '''90''' ||style="background-color: yellow;" | '''381''' || style="background-color: orange;" | 1 229 ||style="background-color: #66ff66;" | 3 695 ||style="background-color: #66ff66;" | 9 800 ||style="background-color: #66ff66;" | 23 304 ||style="background-color: #66ff66;" | 49 757 || style="background-color: #66ff66;" | 103 380 ||style="background-color: #66ff66;" | 196 689 ||style="background-color: #66ff66;" | 350 700 || style="background-color: #66ff66;" | 593 989 | + | | '''14''' ||style="background-color: #81BEF7;" | '''90''' ||style="background-color: yellow;" | '''381''' || style="background-color: orange;" | 1 229 ||style="background-color: #66ff66;" | 3 695 ||style="background-color: #66ff66;" | 9 800 ||style="background-color: #66ff66;" | 23 304 ||style="background-color: #66ff66;" | 49 757 || style="background-color: #66ff66;" | 103 380 ||style="background-color: #66ff66;" | 196 689 ||style="background-color: #66ff66;" | 350 700 || style="background-color: #66ff66;" | 593 989 || style="background-color: #66ff66;" | 996 240 ||style="background-color: #66ff66;" | 1 603 216 ||style="background-color: #66ff66;" | 2 486 227 || style="background-color: #66ff66;" | 3 843 540 |
|- | |- | ||
− | | '''15''' ||style="background-color: #81BEF7;" | '''96''' ||style="background-color: yellow;" | '''448''' ||style="background-color: orange;" | 1 420 ||style="background-color: #66ff66;" | 4 292 ||style="background-color: #66ff66;" | 12 232 ||style="background-color: #66ff66;" | 32 092 ||style="background-color: #66ff66;" | 68 944 ||style="background-color: #66ff66;" | 142 516 ||style="background-color: #66ff66;" | 276 928 ||style="background-color: #66ff66;" | 514 580 ||style="background-color: #66ff66;" | 908 480 | + | | '''15''' ||style="background-color: #81BEF7;" | '''96''' ||style="background-color: yellow;" | '''448''' ||style="background-color: orange;" | 1 420 ||style="background-color: #66ff66;" | 4 292 ||style="background-color: #66ff66;" | 12 232 ||style="background-color: #66ff66;" | 32 092 ||style="background-color: #66ff66;" | 68 944 ||style="background-color: #66ff66;" | 142 516 ||style="background-color: #66ff66;" | 276 928 ||style="background-color: #66ff66;" | 514 580 ||style="background-color: #66ff66;" | 908 480 ||style="background-color: #66ff66;" | 1 550 228 ||style="background-color: #66ff66;" | 2 566 712 ||style="background-color: #66ff66;" | 4 013 468 ||style="background-color: #66ff66;" | 6 155 056 |
|- | |- | ||
− | | '''16''' ||style="background-color: #81BEF7;" | '''112''' ||style="background-color: orange;" | 518 ||style="background-color: #66ff66;" | 1 788 ||style="background-color: #66ff66;" | 5 847 ||style="background-color: #66ff66;" | 17 733 ||style="background-color: #66ff66;" | | + | | '''16''' ||style="background-color: #81BEF7;" | '''112''' ||style="background-color: orange;" | 518 ||style="background-color: #66ff66;" | 1 788 ||style="background-color: #66ff66;" | 5 847 ||style="background-color: #66ff66;" | 17 733 ||style="background-color: #66ff66;" | 45 900 ||style="background-color: #66ff66;" | 107 748 ||style="background-color: #66ff66;" | 232 245 ||style="background-color: #66ff66;" | 479 255 ||style="background-color: #66ff66;" | 924 420 ||style="background-color: #66ff66;" | 1 702 428 ||style="background-color: #66ff66;" | 2 982 623 ||style="background-color: #66ff66;" | 5 209 347 ||style="background-color: #66ff66;" | 8 476 048 ||style="background-color: #66ff66;" | 13 588 848 |
|- | |- | ||
− | | '''17''' ||style="background-color: orange;" | '''130''' ||style="background-color: gold;" | 570 ||style="background-color: gold;" | 1 954 ||style="background-color: #66ff66;" | 6 468 ||style="background-color: #66ff66;" | 20 360 ||style="background-color: #66ff66;" | 57 684 ||style="background-color: #66ff66;" | 136 512 ||style="background-color: #66ff66;" | 321 780 ||style="background-color: #66ff66;" | 659 464 ||style="background-color: #66ff66;" | 1 350 820 ||style="background-color: #66ff66;" | 2 479 104 | + | | '''17''' ||style="background-color: orange;" | '''130''' ||style="background-color: gold;" | 570 ||style="background-color: gold;" | 1 954 ||style="background-color: #66ff66;" | 6 468 ||style="background-color: #66ff66;" | 20 360 ||style="background-color: #66ff66;" | 57 684 ||style="background-color: #66ff66;" | 136 512 ||style="background-color: #66ff66;" | 321 780 ||style="background-color: #66ff66;" | 659 464 ||style="background-color: #66ff66;" | 1 350 820 ||style="background-color: #66ff66;" | 2 479 104 ||style="background-color: #66ff66;" | 4 557 364 ||style="background-color: #66ff66;" | 7 729 000 ||style="background-color: #66ff66;" | 13 275 108 ||style="background-color: #66ff66;" | 21 252 864 |
|- | |- | ||
− | | '''18''' ||style="background-color: orange;" | '''138''' ||style="background-color: gold;" | | + | | '''18''' ||style="background-color: orange;" | '''138''' ||style="background-color: gold;" | 655 ||style="background-color: gold;" | 2 645 ||style="background-color: #66ff66;" | 8 425 ||style="background-color: #66ff66;" | 27 273 ||style="background-color: #66ff66;" | 80 940 ||style="background-color: #66ff66;" | 208 872 ||style="background-color: #66ff66;" | 492 776 ||style="background-color: #66ff66;" | 1 078 280 ||style="background-color: #66ff66;" | 2 202 955 ||style="background-color: #66ff66;" | 4 388 640 ||style="background-color: #66ff66;" | 8 068 383 ||style="background-color: #66ff66;" | 14 718 984 ||style="background-color: #66ff66;" | 25 609 955 ||style="background-color: #66ff66;" | 43 068 508 |
|- | |- | ||
− | | '''19''' ||style="background-color: orange;" | '''156''' ||style="background-color: gold;" | | + | | '''19''' ||style="background-color: orange;" | '''156''' ||style="background-color: gold;" | 722 ||style="background-color: gold;" | 2 696 ||style="background-color: #66ff66;" | 9 652 ||style="background-color: #66ff66;" | 31 440 ||style="background-color: #66ff66;" | 99 420 ||style="background-color: #66ff66;" | 258 040 ||style="background-color: #66ff66;" | 652 004 ||style="background-color: #66ff66;" | 1 416 256 ||style="background-color: #66ff66;" | 3 101 860 ||style="background-color: #66ff66;" | 6 100 520 ||style="background-color: #66ff66;" | 11 797 684 ||style="background-color: #66ff66;" | 21 659 528 ||style="background-color: #66ff66;" | 38 328 220 ||style="background-color: #66ff66;" | 66 601 304 |
|- | |- | ||
− | | '''20''' ||style="background-color: orange;" | '''171''' ||style="background-color: gold;" | | + | | '''20''' ||style="background-color: orange;" | '''171''' ||style="background-color: gold;" | 815 ||style="background-color: gold;" | 3 175 ||style="background-color: #66ff66;" | 12 396 ||style="background-color: #66ff66;" | 42 252 ||style="background-color: #66ff66;" | 132 720 ||style="background-color: #66ff66;" | 371 400 ||style="background-color: #66ff66;" | 930 184 ||style="background-color: #66ff66;" | 2 232 648 ||style="background-color: #66ff66;" | 4 947 880 ||style="background-color: #66ff66;" | 10 238 745 ||style="background-color: #66ff66;" | 20 452 920 ||style="background-color: #66ff66;" | 38 155 632 ||style="background-color: #66ff66;" | 70 612 644 ||style="background-color: #66ff66;" | 126 967 008 |
|} | |} | ||
</center> | </center> | ||
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<center> | <center> | ||
{| border="1" | {| border="1" | ||
− | | '''<math>d</math>\<math>k</math>'''|| '''2''' || '''3''' || '''4'''|| '''5''' || '''6''' || '''7''' || '''8''' || '''9''' || '''10''' || '''11''' || '''12''' | + | | '''<math>d</math>\<math>k</math>'''|| '''2''' || '''3''' || '''4'''|| '''5''' || '''6''' || '''7''' || '''8''' || '''9''' || '''10''' || '''11''' || '''12''' || '''13''' || '''14''' || '''15''' || '''16''' |
|- | |- | ||
|'''3''' | |'''3''' | ||
Line 128: | Line 128: | ||
{| border="2" style="background:rgb(180,180,255);" | {| border="2" style="background:rgb(180,180,255);" | ||
|36 | |36 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |40 | ||
|- | |- | ||
|'''100%''' | |'''100%''' | ||
Line 145: | Line 151: | ||
| align="center" | | | align="center" | | ||
{| border="2" style="background:rgb(180,180,255);" | {| border="2" style="background:rgb(180,180,255);" | ||
− | | | + | |52 |
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |56 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |60 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |64 | ||
|- | |- | ||
|'''100%''' | |'''100%''' | ||
Line 217: | Line 241: | ||
{| border="2" style="background:rgb(180,180,255);" | {| border="2" style="background:rgb(180,180,255);" | ||
|313 | |313 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |365 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |421 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |481 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |545 | ||
|- | |- | ||
|'''100%''' | |'''100%''' | ||
Line 288: | Line 336: | ||
{| border="2" style="background:rgb(180,180,255);" | {| border="2" style="background:rgb(180,180,255);" | ||
|576 | |576 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |676 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |784 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |900 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |1024 | ||
|- | |- | ||
|'''100%''' | |'''100%''' | ||
Line 359: | Line 431: | ||
{| border="2" style="background:rgb(180,180,255);" | {| border="2" style="background:rgb(180,180,255);" | ||
|2 329 | |2 329 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |2 943 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |3 629 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |4 431 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | |5 357 | ||
|- | |- | ||
|'''100%''' | |'''100%''' | ||
Line 430: | Line 526: | ||
{| border="2" style="background:#ABCDEF;" | {| border="2" style="background:#ABCDEF;" | ||
|4 672 | |4 672 | ||
+ | |- | ||
+ | |89% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |5 928 | ||
+ | |- | ||
+ | |88% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |7 392 | ||
+ | |- | ||
+ | |88% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |9 080 | ||
+ | |- | ||
+ | |89% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |11 008 | ||
|- | |- | ||
|89% | |89% | ||
Line 501: | Line 621: | ||
{| border="2" style="background:#ABCDEF;" | {| border="2" style="background:#ABCDEF;" | ||
|16 641 | |16 641 | ||
+ | |- | ||
+ | |75% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |22 569 | ||
+ | |- | ||
+ | |75% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |29 961 | ||
+ | |- | ||
+ | |75% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |39 041 | ||
+ | |- | ||
+ | |75% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |50 049 | ||
|- | |- | ||
|75% | |75% | ||
Line 572: | Line 716: | ||
{| border="2" style="background:#ABCDEF;" | {| border="2" style="background:#ABCDEF;" | ||
|28 610 | |28 610 | ||
+ | |- | ||
+ | |74% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |39 210 | ||
+ | |- | ||
+ | |74% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |52 530 | ||
+ | |- | ||
+ | |74% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |69 002 | ||
+ | |- | ||
+ | |74% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |89 090 | ||
|- | |- | ||
|74% | |74% | ||
Line 593: | Line 761: | ||
|} | |} | ||
| align="center" | | | align="center" | | ||
− | {| border="2" style="background: | + | {| border="2" style="background:rgb(180,180,255);" |
− | | | + | |457 |
|- | |- | ||
− | | | + | |'''100%''' |
|} | |} | ||
| align="center" | | | align="center" | | ||
− | {| border="2" style="background: | + | {| border="2" style="background:rgb(180,180,255);" |
− | |1 | + | |1 099 |
|- | |- | ||
− | | | + | |'''100%''' |
|} | |} | ||
| align="center" | | | align="center" | | ||
Line 643: | Line 811: | ||
{| border="2" style="background:#ABCDEF;" | {| border="2" style="background:#ABCDEF;" | ||
|85 305 | |85 305 | ||
+ | |- | ||
+ | |62% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |124 515 | ||
+ | |- | ||
+ | |62% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |177 045 | ||
+ | |- | ||
+ | |62% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |246 047 | ||
+ | |- | ||
+ | |62% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |335 137 | ||
|- | |- | ||
|62% | |62% | ||
Line 664: | Line 856: | ||
|} | |} | ||
| align="center" | | | align="center" | | ||
− | {| border="2" style="background: | + | {| border="2" style="background:rgb(180,180,255);" |
− | | | + | |576 |
|- | |- | ||
− | | | + | |'''100%''' |
|} | |} | ||
| align="center" | | | align="center" | | ||
Line 714: | Line 906: | ||
{| border="2" style="background:#ABCDEF;" | {| border="2" style="background:#ABCDEF;" | ||
|142 000 | |142 000 | ||
+ | |- | ||
+ | |61% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |209 820 | ||
+ | |- | ||
+ | |61% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |301 560 | ||
+ | |- | ||
+ | |61% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |423 092 | ||
+ | |- | ||
+ | |61% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |581 184 | ||
|- | |- | ||
|61% | |61% | ||
Line 787: | Line 1,003: | ||
|- | |- | ||
|52% | |52% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |579 125 | ||
+ | |- | ||
+ | |51% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |880 685 | ||
+ | |- | ||
+ | |51% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |1 303 777 | ||
+ | |- | ||
+ | |51% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |1 884 961 | ||
+ | |- | ||
+ | |51% | ||
|} | |} | ||
|- | |- | ||
Line 855: | Line 1,095: | ||
| align="center" | | | align="center" | | ||
{| border="2" style="background:#ABCDEF;" | {| border="2" style="background:#ABCDEF;" | ||
− | | | + | |596 610 |
+ | |- | ||
+ | |50% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |948 430 | ||
+ | |- | ||
+ | |50% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |1 459 810 | ||
+ | |- | ||
+ | |50% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |2 184 462 | ||
+ | |- | ||
+ | |50% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | |3 188 738 | ||
|- | |- | ||
|50% | |50% | ||
Line 929: | Line 1,193: | ||
|- | |- | ||
|43% | |43% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 2 340 495 | ||
+ | |- | ||
+ | |43% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 3 800 305 | ||
+ | |- | ||
+ | |42% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 5 984 767 | ||
+ | |- | ||
+ | |42% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 9 173 505 | ||
+ | |- | ||
+ | |42% | ||
|} | |} | ||
|- | |- | ||
Line 1,000: | Line 1,288: | ||
|- | |- | ||
|42% | |42% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 3 732 560 | ||
+ | |- | ||
+ | |42% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 6 140 800 | ||
+ | |- | ||
+ | |42% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 9 785 072 | ||
+ | |- | ||
+ | |41% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 15 158 272 | ||
+ | |- | ||
+ | |41% | ||
|} | |} | ||
|- | |- | ||
Line 1,040: | Line 1,352: | ||
| 108 545 | | 108 545 | ||
|- | |- | ||
− | | | + | |42% |
|} | |} | ||
| align="center" | | | align="center" | | ||
Line 1,072: | Line 1,384: | ||
|36% | |36% | ||
|} | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 8 405 905 | ||
+ | |- | ||
+ | |35% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 14 546 705 | ||
+ | |- | ||
+ | |36% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 24 331 777 | ||
+ | |- | ||
+ | |35% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 39 490 049 | ||
+ | |- | ||
+ | |34% | ||
+ | |} | ||
+ | |||
|- | |- | ||
+ | |||
Line 1,106: | Line 1,444: | ||
|38% | |38% | ||
|} | |} | ||
+ | |||
| align="center" | | | align="center" | | ||
{| border="2" style="background:#ABCDEF;" | {| border="2" style="background:#ABCDEF;" | ||
Line 1,141: | Line 1,480: | ||
|- | |- | ||
|35% | |35% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 13 079 250 | ||
+ | |- | ||
+ | |35% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 22 952 610 | ||
+ | |- | ||
+ | |34% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 38 878 482 | ||
+ | |- | ||
+ | |34% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 63 821 826 | ||
+ | |- | ||
+ | |33% | ||
+ | |} | ||
+ | |- | ||
+ | |||
+ | |||
+ | |||
+ | |'''18''' | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | | 138 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 1 159 | ||
+ | |- | ||
+ | |57% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 5 641 | ||
+ | |- | ||
+ | |47% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 22 363 | ||
+ | |- | ||
+ | |38% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 75 517 | ||
+ | |- | ||
+ | |36% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 224 143 | ||
+ | |- | ||
+ | |36% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 598 417 | ||
+ | |- | ||
+ | |35% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 1 462 563 | ||
+ | |- | ||
+ | |34% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 3 317 445 | ||
+ | |- | ||
+ | |33% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 7 059 735 | ||
+ | |- | ||
+ | |31% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 14 218 905 | ||
+ | |- | ||
+ | |31% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 27 298 155 | ||
+ | |- | ||
+ | |30% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 50 250 765 | ||
+ | |- | ||
+ | |29% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 89 129 247 | ||
+ | |- | ||
+ | |29% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 152 951 073 | ||
+ | |- | ||
+ | |28% | ||
+ | |} | ||
+ | |- | ||
+ | |||
+ | |||
+ | |||
+ | |'''19''' | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | | 156 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 1 340 | ||
+ | |- | ||
+ | |54% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 6 800 | ||
+ | |- | ||
+ | |40% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 28 004 | ||
+ | |- | ||
+ | |34% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 97 880 | ||
+ | |- | ||
+ | |32% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 299 660 | ||
+ | |- | ||
+ | |33% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 822 560 | ||
+ | |- | ||
+ | |31% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 2 060 980 | ||
+ | |- | ||
+ | |32% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 4 780 008 | ||
+ | |- | ||
+ | |30% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 10 377 180 | ||
+ | |- | ||
+ | |30% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 21 278 640 | ||
+ | |- | ||
+ | |29% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 41 517 060 | ||
+ | |- | ||
+ | |28% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 77 548 920 | ||
+ | |- | ||
+ | |28% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 139 380 012 | ||
+ | |- | ||
+ | |27% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 242 080 320 | ||
+ | |- | ||
+ | |28% | ||
+ | |} | ||
+ | |- | ||
+ | |||
+ | |||
+ | |||
+ | |'''20''' | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:rgb(180,180,255);" | ||
+ | | 171 | ||
+ | |- | ||
+ | |'''100%''' | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 1 561 | ||
+ | |- | ||
+ | |52% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 8 361 | ||
+ | |- | ||
+ | |38% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 36 365 | ||
+ | |- | ||
+ | |34% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 134 245 | ||
+ | |- | ||
+ | |31% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 433 905 | ||
+ | |- | ||
+ | |31% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 1 256 465 | ||
+ | |- | ||
+ | |30% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 3 317 445 | ||
+ | |- | ||
+ | |28% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 8 097 453 | ||
+ | |- | ||
+ | |28% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 18 474 633 | ||
+ | |- | ||
+ | |27% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 39 753 273 | ||
+ | |- | ||
+ | |26% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 81 270 333 | ||
+ | |- | ||
+ | |25% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 158 819 253 | ||
+ | |- | ||
+ | |24% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 298 199 265 | ||
+ | |- | ||
+ | |24% | ||
+ | |} | ||
+ | | align="center" | | ||
+ | {| border="2" style="background:#ABCDEF;" | ||
+ | | 540 279 585 | ||
+ | |- | ||
+ | |24% | ||
|} | |} | ||
Latest revision as of 09:24, 24 November 2019
Table of the orders of the largest known circulant graphs
[math]d[/math]\[math]k[/math] | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
3 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56 | 60 | 64 |
4 | 13 | 25 | 41 | 61 | 85 | 113 | 145 | 181 | 221 | 265 | 313 | 365 | 421 | 481 | 545 |
5 | 16 | 36 | 64 | 100 | 144 | 196 | 256 | 324 | 400 | 484 | 576 | 676 | 784 | 900 | 1 024 |
6 | 21 | 55 | 117 | 203 | 333 | 515 | 737 | 1 027 | 1 393 | 1 815 | 2 329 | 2 943 | 3 629 | 4 431 | 5 357 |
7 | 26 | 76 | 160 | 308 | 536 | 828 | 1 232 | 1 764 | 2 392 | 3 180 | 4 144 | 5 236 | 6 536 | 8 060 | 9 744 |
8 | 35 | 104 | 248 | 528 | 984 | 1 712 | 2 768 | 4 280 | 6 320 | 9 048 | 12 552 | 17 024 | 22 568 | 29 408 | 37 664 |
9 | 42 | 130 | 320 | 700 | 1 416 | 2 548 | 4 304 | 6 804 | 10 320 | 15 004 | 21 192 | 29 068 | 39 032 | 51 300 | 66 336 |
10 | 51 | 177 | 457 | 1 099 | 2 380 | 4 551 | 8 288 | 14 099 | 22 805 | 35 568 | 53 025 | 77 572 | 110 045 | 152 671 | 208 052 |
11 | 56 | 210 | 576 | 1 428 | 3 200 | 6 652 | 12 416 | 21 572 | 35 880 | 56 700 | 87 248 | 128 852 | 184 424 | 259 260 | 355 576 |
12 | 67 | 275 | 819 | 2 120 | 5 044 | 10 777 | 21 384 | 39 996 | 69 965 | 117 712 | 190 392 | 295 840 | 448 920 | 662 680 | 952 985 |
13 | 80 | 312 | 970 | 2 676 | 6 256 | 14 740 | 30 760 | 57 396 | 106 120 | 182 980 | 295 840 | 476 100 | 732 744 | 1 081 860 | 1 593 064 |
14 | 90 | 381 | 1 229 | 3 695 | 9 800 | 23 304 | 49 757 | 103 380 | 196 689 | 350 700 | 593 989 | 996 240 | 1 603 216 | 2 486 227 | 3 843 540 |
15 | 96 | 448 | 1 420 | 4 292 | 12 232 | 32 092 | 68 944 | 142 516 | 276 928 | 514 580 | 908 480 | 1 550 228 | 2 566 712 | 4 013 468 | 6 155 056 |
16 | 112 | 518 | 1 788 | 5 847 | 17 733 | 45 900 | 107 748 | 232 245 | 479 255 | 924 420 | 1 702 428 | 2 982 623 | 5 209 347 | 8 476 048 | 13 588 848 |
17 | 130 | 570 | 1 954 | 6 468 | 20 360 | 57 684 | 136 512 | 321 780 | 659 464 | 1 350 820 | 2 479 104 | 4 557 364 | 7 729 000 | 13 275 108 | 21 252 864 |
18 | 138 | 655 | 2 645 | 8 425 | 27 273 | 80 940 | 208 872 | 492 776 | 1 078 280 | 2 202 955 | 4 388 640 | 8 068 383 | 14 718 984 | 25 609 955 | 43 068 508 |
19 | 156 | 722 | 2 696 | 9 652 | 31 440 | 99 420 | 258 040 | 652 004 | 1 416 256 | 3 101 860 | 6 100 520 | 11 797 684 | 21 659 528 | 38 328 220 | 66 601 304 |
20 | 171 | 815 | 3 175 | 12 396 | 42 252 | 132 720 | 371 400 | 930 184 | 2 232 648 | 4 947 880 | 10 238 745 | 20 452 920 | 38 155 632 | 70 612 644 | 126 967 008 |
The following table is the key to the colors in the table presented above:
Color | Details |
* | Numbers in bold indicate graphs known to be optimal. |
* | Optimal graphs. |
* | Optimal graphs found by E. Monakhova. |
* | Graphs found by H. Macbeth, J. Šiagiová, J. Širáň and T. Vetrík. |
* | Graphs found by R. Dougherty and V. Faber and independently for d=6 by E. Monakhova. |
* | Graphs found by B. McKay. |
* | Graphs found by R. Lewis. |
* | Graphs found by R. Lewis and independently by R. Feria-Puron, H. Pérez-Rosés and J. Ryan. |
* | Graphs found by R. Feria-Puron, H. Pérez-Rosés and J. Ryan. |
* | Graphs found by D. Bevan, G. Erskine and R. Lewis. |
* | Graphs found by G. Erskine. |
* | Graphs found by O. Monakhov and E. Monakhova. |
Table of the lowest upper bounds known at present, and the percentage of the order of the largest known graphs
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References
- D. Bevan, G. Erskine, and R. Lewis. Large circulant graphs of fixed diameter and arbitrary degree. ArXiv
- R. Feria-Puron, J. Ryan, and H. Perez-Roses. Searching for Large Multi-Loop Networks. Electronic Notes in Discrete Mathematics, vol. 46 (2014), pp. 233-240. doi:10.1016/j.endm.2014.08.031. Link to journal
- R.R. Lewis. The Degree/Diameter Problem for Circulant Graphs of Degree 8 and 9. The Electronic Journal of Combinatorics, vol. 21(4) (2014), #P4.50. Link to journal
- E.A. Monakhova, Synthesis of optimal Diophantine structures, Comput. Syst. Novosibirsk , 80 (1979), p.18--35. (in Russian).
- E. Monakhova, Optimal Triple Loop Networks with Given Transmission Delay: Topological Design and Routing, Inter. Network Optimization Conference, (INOC'2003), Evry/Paris, France, (2003), p.410--415.
- E.A. Monakhova . On synthesis of multidimensional circulant graphs of diameter two, Bulletin of the Tomsk Polytechnic University. 323(2) (2013), p.25--28. (in Russian). Link to journal