Temp VertexTransitive - Revision history

Grahame at 07:49, 16 July 2023

2023-07-16T07:49:52Z

Grahame: /* Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem */

2022-02-24T18:00:20Z

‎Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem

Grahame: /* Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem */

2022-02-24T13:54:43Z

‎Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem

Grahame: /* Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem */

2022-02-22T17:54:54Z

‎Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem

Grahame: /* Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem */

2022-02-20T16:20:45Z

‎Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem

Grahame at 18:38, 19 February 2022

2022-02-19T18:38:45Z

Grahame: /* Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem */

2022-02-19T18:36:42Z

‎Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem

Grahame: /* Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem */

2022-02-19T18:23:26Z

‎Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem

Grahame: /* Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem */

2022-02-19T18:21:25Z

‎Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem

Grahame: /* Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem */

2022-02-19T18:18:15Z

‎Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem

@@ Line 3: / Line 3: @@
 ===Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem===
-Below is the table of the largest known vertex-transitive graphs in the undirected [[The Degree/Diameter Problem | degree diameter problem]] for graphs of [http://en.wikipedia.org/wiki/Degree_(graph_theory) degree] 3&nbsp;≤&nbsp;''d''&nbsp;≤&nbsp;20 and [http://en.wikipedia.org/wiki/Distance_(graph_theory) diameter] 2&nbsp;≤&nbsp;''k''&nbsp;≤&nbsp;10. All graphs which are known to be optimal are marked in bold.
+Below is the table of the largest known vertex-transitive graphs in the undirected [[The Degree/Diameter Problem | degree diameter problem]] for graphs of [http://en.wikipedia.org/wiki/Degree_(graph_theory) degree] 3&nbsp;≤&nbsp;''d''&nbsp;≤&nbsp;20 and [http://en.wikipedia.org/wiki/Distance_(graph_theory) diameter] 2&nbsp;≤&nbsp;''k''&nbsp;≤&nbsp;10. All graphs which are known to be optimal are marked in '''bold'''.
 <center>

@@ Line 12: / Line 12: @@
 |-
-| '''4''' ||style="background-color: #eee;" | '''13''' ||style="background-color: #eee;" | 30 ||style="background-color: #eee;" | 84 || style="background-color: #eee;" | 216 ||style="background-color: #eee;" | 513||style="background-color: #eee;" | 1 155 ||style="background-color: #eee;" | 3 080 ||style="background-color: #eee;" | 7 550 ||style="background-color: #eee;" | 17 604
+| '''4''' ||style="background-color: #eee;" | '''13''' ||style="background-color: #8f0;" | 35 ||style="background-color: #eee;" | 84 || style="background-color: #8f0;" | 273 ||style="background-color: #eee;" | 513||style="background-color: #eee;" | 1 155 ||style="background-color: #eee;" | 3 080 ||style="background-color: #eee;" | 7 550 ||style="background-color: #eee;" | 17 604
 |-
 | '''5''' ||style="background-color: #eee;" | 18 ||style="background-color: #eee;" | 60 ||style="background-color: #eee;" | 210 ||style="background-color: #eee;" |  546||style="background-color: #eee;" | 1 640 ||style="background-color: #eee;" |  5 500 ||style="background-color: #eee;" |  16 965 ||style="background-color: #eee;" |  57 840 ||style="background-color: #eee;" |  187 056
@@ Line 66: / Line 66: @@
 |-
 |style="background-color: #f80; text-align: center;" | * || See B. D. McKay, M. Miller and J. Širáň, ''A note on large graphs of diameter two and given maximum degree''.
 |}
 </center>

@@ Line 16: / Line 16: @@
 | '''5''' ||style="background-color: #eee;" | 18 ||style="background-color: #eee;" | 60 ||style="background-color: #eee;" | 210 ||style="background-color: #eee;" |  546||style="background-color: #eee;" | 1 640 ||style="background-color: #eee;" |  5 500 ||style="background-color: #eee;" |  16 965 ||style="background-color: #eee;" |  57 840 ||style="background-color: #eee;" |  187 056
 |-
-| '''6''' || style="background-color: #eee;" | 32 ||style="background-color: #eee;" | 108 ||style="background-color: #eee;" | 375 ||style="background-color: #eee;" | 1 395 ||style="background-color: #eee;" | 5 115 ||style="background-color: #eee;" | 19 383 ||style="background-color: #eee;" | 76 461 ||style="background-color: #eee;" | 307 845 ||style="background-color: #eee;" | 1 253 615
+| '''6''' || style="background-color: #eee;" | '''32''' ||style="background-color: #eee;" | 108 ||style="background-color: #eee;" | 375 ||style="background-color: #eee;" | 1 395 ||style="background-color: #eee;" | 5 115 ||style="background-color: #eee;" | 19 383 ||style="background-color: #eee;" | 76 461 ||style="background-color: #eee;" | 307 845 ||style="background-color: #eee;" | 1 253 615
 |-
 | '''7''' ||style="background-color: #0ff;" |'''50''' ||style="background-color: #eee;" |168 ||style="background-color: #eee;" | 672 ||style="background-color: #eee;" | 2 756 ||style="background-color: #eee;" | 11 988 ||style="background-color: #eee;" | 52 768 ||style="background-color: #eee;" | 249 660 ||style="background-color: #eee;" | 1 223 050 ||style="background-color: #eee;" | 6 007 230

@@ Line 12: / Line 12: @@
 |-
-| '''4''' ||style="background-color: #eee;" | '''13''' ||style="background-color: #eee;" | '''30''' ||style="background-color: #eee;" | '''84''' || style="background-color: #eee;" | 216 ||style="background-color: #eee;" | 513||style="background-color: #eee;" | 1 155 ||style="background-color: #eee;" | 3 080 ||style="background-color: #eee;" | 7 550 ||style="background-color: #eee;" | 17 604
+| '''4''' ||style="background-color: #eee;" | '''13''' ||style="background-color: #eee;" | 30 ||style="background-color: #eee;" | 84 || style="background-color: #eee;" | 216 ||style="background-color: #eee;" | 513||style="background-color: #eee;" | 1 155 ||style="background-color: #eee;" | 3 080 ||style="background-color: #eee;" | 7 550 ||style="background-color: #eee;" | 17 604
 |-
-| '''5''' ||style="background-color: #eee;" | '''18''' ||style="background-color: #eee;" | '''60''' ||style="background-color: #eee;" | 210 ||style="background-color: #eee;" |  546||style="background-color: #eee;" | 1 640 ||style="background-color: #eee;" |  5 500 ||style="background-color: #eee;" |  16 965 ||style="background-color: #eee;" |  57 840 ||style="background-color: #eee;" |  187 056
+| '''5''' ||style="background-color: #eee;" | 18 ||style="background-color: #eee;" | 60 ||style="background-color: #eee;" | 210 ||style="background-color: #eee;" |  546||style="background-color: #eee;" | 1 640 ||style="background-color: #eee;" |  5 500 ||style="background-color: #eee;" |  16 965 ||style="background-color: #eee;" |  57 840 ||style="background-color: #eee;" |  187 056
 |-
-| '''6''' || style="background-color: #eee;" |'''32'''||style="background-color: #eee;" | '''108''' ||style="background-color: #eee;" | 375 ||style="background-color: #eee;" | 1 395 ||style="background-color: #eee;" | 5 115 ||style="background-color: #eee;" | 19 383 ||style="background-color: #eee;" | 76 461 ||style="background-color: #eee;" | 307 845 ||style="background-color: #eee;" | 1 253 615
+| '''6''' || style="background-color: #eee;" | 32 ||style="background-color: #eee;" | 108 ||style="background-color: #eee;" | 375 ||style="background-color: #eee;" | 1 395 ||style="background-color: #eee;" | 5 115 ||style="background-color: #eee;" | 19 383 ||style="background-color: #eee;" | 76 461 ||style="background-color: #eee;" | 307 845 ||style="background-color: #eee;" | 1 253 615
 |-
-| '''7''' ||style="background-color: #0ff;" |'''50''' ||style="background-color: #eee;" |'''168''' ||style="background-color: #eee;" | 672 ||style="background-color: #eee;" | 2 756 ||style="background-color: #eee;" | 11 988 ||style="background-color: #eee;" | 52 768 ||style="background-color: #eee;" | 249 660 ||style="background-color: #eee;" | 1 223 050 ||style="background-color: #eee;" | 6 007 230
+| '''7''' ||style="background-color: #0ff;" |'''50''' ||style="background-color: #eee;" |168 ||style="background-color: #eee;" | 672 ||style="background-color: #eee;" | 2 756 ||style="background-color: #eee;" | 11 988 ||style="background-color: #eee;" | 52 768 ||style="background-color: #eee;" | 249 660 ||style="background-color: #eee;" | 1 223 050 ||style="background-color: #eee;" | 6 007 230
 |-
-| '''8''' ||style="background-color: #eee;" |'''48'''||style="background-color: #eee;" | 253 ||style="background-color: #eee;" | 1 100 ||style="background-color: #eee;" | 5 060 ||style="background-color: #eee;" | 23 991 ||style="background-color: #eee;" | 131 137 ||style="background-color: #eee;" | 734 820 ||style="background-color: #eee;" | 4 243 100 ||style="background-color: #eee;" | 24 897 161
+| '''8''' ||style="background-color: #eee;" | 48 ||style="background-color: #eee;" | 253 ||style="background-color: #eee;" | 1 100 ||style="background-color: #eee;" | 5 060 ||style="background-color: #eee;" | 23 991 ||style="background-color: #eee;" | 131 137 ||style="background-color: #eee;" | 734 820 ||style="background-color: #eee;" | 4 243 100 ||style="background-color: #eee;" | 24 897 161
 |-
-| '''9''' ||style="background-color: #eee;" | '''60''' || style="background-color: #eee;" | 294 ||style="background-color: #eee;" | 1 550 ||style="background-color: #eee;" | 8 200 ||style="background-color: #eee;" | 45 612 ||style="background-color: #eee;" | 279 616 ||style="background-color: #eee;" | 1 686 600 ||style="background-color: #eee;" | 12 123 288 ||style="background-color: #eee;" | 65 866 350
+| '''9''' ||style="background-color: #eee;" | 60 || style="background-color: #eee;" | 294 ||style="background-color: #eee;" | 1 550 ||style="background-color: #eee;" | 8 200 ||style="background-color: #eee;" | 45 612 ||style="background-color: #eee;" | 279 616 ||style="background-color: #eee;" | 1 686 600 ||style="background-color: #eee;" | 12 123 288 ||style="background-color: #eee;" | 65 866 350
 |-
-| '''10''' ||style="background-color: #eee;" | '''72''' || style="background-color: #eee;" | 406 ||style="background-color: #eee;" | 2 286 ||style="background-color: #eee;" | 13 140 ||style="background-color: #eee;" | 81 235 ||style="background-color: #eee;" | 583 083 ||style="background-color: #eee;" | 4 293 452 ||style="background-color: #eee;" | 27 997 191 ||style="background-color: #eee;" | 201 038 922
+| '''10''' ||style="background-color: #eee;" | 72 || style="background-color: #eee;" | 406 ||style="background-color: #eee;" | 2 286 ||style="background-color: #eee;" | 13 140 ||style="background-color: #eee;" | 81 235 ||style="background-color: #eee;" | 583 083 ||style="background-color: #eee;" | 4 293 452 ||style="background-color: #eee;" | 27 997 191 ||style="background-color: #eee;" | 201 038 922
 |-
-| '''11''' ||style="background-color: #eee;" | '''84''' ||style="background-color: #eee;" | 486 || style="background-color: #eee;" | 2 860 ||style="background-color: #eee;" | 19 500 ||style="background-color: #eee;" | 139 446 ||style="background-color: #eee;" | 1 001 268 ||style="background-color: #eee;" | 7 442 328 || style="background-color: #eee;" | 72 933 102 ||style="background-color: #eee;" |  500 605 110
+| '''11''' ||style="background-color: #eee;" | 84 ||style="background-color: #eee;" | 486 || style="background-color: #eee;" | 2 860 ||style="background-color: #eee;" | 19 500 ||style="background-color: #eee;" | 139 446 ||style="background-color: #eee;" | 1 001 268 ||style="background-color: #eee;" | 7 442 328 || style="background-color: #eee;" | 72 933 102 ||style="background-color: #eee;" |  500 605 110
 |-
-| '''12''' ||style="background-color: #eee;" | '''96''' ||style="background-color: #eee;" | 605 ||style="background-color: #eee;" | 3 775 ||style="background-color: #eee;" | 29 470||style="background-color: #eee;" | 229 087 ||style="background-color: #eee;" | 1 999 500 ||style="background-color: #eee;" | 15 924 326  ||style="background-color: #eee;" | 158 158 875 ||style="background-color: #eee;" | 1 225 374 192
+| '''12''' ||style="background-color: #eee;" | 96 ||style="background-color: #eee;" | 605 ||style="background-color: #eee;" | 3 775 ||style="background-color: #eee;" | 29 470||style="background-color: #eee;" | 229 087 ||style="background-color: #eee;" | 1 999 500 ||style="background-color: #eee;" | 15 924 326  ||style="background-color: #eee;" | 158 158 875 ||style="background-color: #eee;" | 1 225 374 192
 |-
 | '''13''' ||style="background-color: #f80;" | 162 ||style="background-color: #eee;" | 680 ||style="background-color: #eee;" | 4 788 ||style="background-color: #eee;" |40 260 ||style="background-color: #eee;" | 347 126 ||style="background-color: #eee;" | 3 322 080 ||style="background-color: #eee;" | 29 927 790  ||style="background-color: #eee;" | 233 660 788 ||style="background-color: #eee;" | 2 129 329 324

@@ Line 18: / Line 18: @@
 | '''6''' || style="background-color: #eee;" |'''32'''||style="background-color: #eee;" | '''108''' ||style="background-color: #eee;" | 375 ||style="background-color: #eee;" | 1 395 ||style="background-color: #eee;" | 5 115 ||style="background-color: #eee;" | 19 383 ||style="background-color: #eee;" | 76 461 ||style="background-color: #eee;" | 307 845 ||style="background-color: #eee;" | 1 253 615
 |-
-| '''7''' ||style="background-color: #eee;" |'''36''' ||style="background-color: #eee;" |'''168''' ||style="background-color: #eee;" | 672 ||style="background-color: #eee;" | 2 756 ||style="background-color: #eee;" | 11 988 ||style="background-color: #eee;" | 52 768 ||style="background-color: #eee;" | 249 660 ||style="background-color: #eee;" | 1 223 050 ||style="background-color: #eee;" | 6 007 230
+| '''7''' ||style="background-color: #0ff;" |'''50''' ||style="background-color: #eee;" |'''168''' ||style="background-color: #eee;" | 672 ||style="background-color: #eee;" | 2 756 ||style="background-color: #eee;" | 11 988 ||style="background-color: #eee;" | 52 768 ||style="background-color: #eee;" | 249 660 ||style="background-color: #eee;" | 1 223 050 ||style="background-color: #eee;" | 6 007 230
 |-
 | '''8''' ||style="background-color: #eee;" |'''48'''||style="background-color: #eee;" | 253 ||style="background-color: #eee;" | 1 100 ||style="background-color: #eee;" | 5 060 ||style="background-color: #eee;" | 23 991 ||style="background-color: #eee;" | 131 137 ||style="background-color: #eee;" | 734 820 ||style="background-color: #eee;" | 4 243 100 ||style="background-color: #eee;" | 24 897 161
@@ Line 30: / Line 30: @@
 | '''12''' ||style="background-color: #eee;" | '''96''' ||style="background-color: #eee;" | 605 ||style="background-color: #eee;" | 3 775 ||style="background-color: #eee;" | 29 470||style="background-color: #eee;" | 229 087 ||style="background-color: #eee;" | 1 999 500 ||style="background-color: #eee;" | 15 924 326  ||style="background-color: #eee;" | 158 158 875 ||style="background-color: #eee;" | 1 225 374 192
 |-
-| '''13''' ||style="background-color: #eee;" | 112 ||style="background-color: #eee;" | 680 ||style="background-color: #eee;" | 4 788 ||style="background-color: #eee;" |40 260 ||style="background-color: #eee;" | 347 126 ||style="background-color: #eee;" | 3 322 080 ||style="background-color: #eee;" | 29 927 790  ||style="background-color: #eee;" | 233 660 788 ||style="background-color: #eee;" | 2 129 329 324
+| '''13''' ||style="background-color: #f80;" | 162 ||style="background-color: #eee;" | 680 ||style="background-color: #eee;" | 4 788 ||style="background-color: #eee;" |40 260 ||style="background-color: #eee;" | 347 126 ||style="background-color: #eee;" | 3 322 080 ||style="background-color: #eee;" | 29 927 790  ||style="background-color: #eee;" | 233 660 788 ||style="background-color: #eee;" | 2 129 329 324
 |-
 | '''14''' ||style="background-color: #eee;" | 128 ||style="background-color: #eee;" | 873 ||style="background-color: #eee;" | 6 510 ||style="background-color: #eee;" | 57 837 ||style="background-color: #eee;" | 530 448 ||style="background-color: #eee;" | 5 600 532 ||style="background-color: #eee;" | 50 128 239 ||style="background-color: #eee;" | 579 328 377 ||style="background-color: #eee;" | 7 041 746 081
@@ Line 44: / Line 44: @@
 |-
-| '''19''' ||style="background-color: #eee;" | 200 ||style="background-color: #eee;" | 1 638  ||style="background-color: #eee;" | 17 658 ||style="background-color: #eee;" | 221 676 || style="background-color: #eee;" | 3 030 544 || style="background-color: #eee;" | 39 123 116 ||style="background-color: #eee;" | 501 001 000  ||style="background-color: #eee;" | 8 855 580 344 ||style="background-color: #eee;" |
+| '''19''' ||style="background-color: #f80;" | 338 ||style="background-color: #eee;" | 1 638  ||style="background-color: #eee;" | 17 658 ||style="background-color: #eee;" | 221 676 || style="background-color: #eee;" | 3 030 544 || style="background-color: #eee;" | 39 123 116 ||style="background-color: #eee;" | 501 001 000  ||style="background-color: #eee;" | 8 855 580 344 ||style="background-color: #eee;" |
 |-
@@ Line 62: / Line 62: @@
 |-
 |style="background-color: #ff0; text-align: center;" | * || See P. Potočnik, P. Spiga and G. Verret, ''Cubic vertex-transitive graphs on up to 1280 vertices''.
 |}
 </center>

← Older revision		Revision as of 18:38, 19 February 2022
Line 1:		Line 1:
−	This is ~~a temporary page for tables of vertex-transitive graphs in the degree-diameter problem~~.	+	'''NB This page is incomplete and still under construction.'''

	===Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem===		===Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem===

@@ Line 9: / Line 9: @@
 | '''<math>d</math>\<math>k</math>'''||  '''2''' ||  '''3''' ||  '''4'''|| '''5''' ||  '''6''' || '''7''' ||  '''8''' ||  '''9''' ||  '''10'''
 |-
-| '''3''' || style="background-color: #eee;" | '''8''' || style="background-color: #eee;" | '''14''' || style="background-color: #eee;" | '''24''' ||style="background-color: #eee;" | '''60''' || style="background-color: #eee;" | '''72''' ||style="background-color: #eee;" | '''168''' ||style="background-color: #eee;" | '''300'''||style="background-color: #eee;" | 506||style="background-color: #eee;" | 882
+| '''3''' || style="background-color: #f0f;" | '''10''' || style="background-color: #eee;" | '''14''' || style="background-color: #ff0;" | '''30''' ||style="background-color: #eee;" | '''60''' || style="background-color: #ff0;" | '''82''' ||style="background-color: #eee;" | '''168''' ||style="background-color: #eee;" | '''300'''||style="background-color: #ff0;" | 546 ||style="background-color: #ff0;" | 1 250
 |-
@@ Line 59: / Line 59: @@
 |style="background-color: #eee; text-align: center;" | * || Cayley graphs; see the [[The_Degree_Diameter_Problem_for_Cayley_Graphs | separate page]] for details.
 |-
-|style="background-color: #FF0066; text-align: center;" | * || Graphs found by Michael J. Dinneen and Paul Hafner. More details are available in a paper by the authors.
+|style="background-color: #f0f; text-align: center;" | * || The [https://mathworld.wolfram.com/PetersenGraph.html Petersen graph].
 |-
-|style="background-color: #993300; text-align: center;" | * || Graph found by Mitjana M. and Francesc Comellas. This graph was also found independently by Michael Sampels.
+|style="background-color: #ff0; text-align: center;" | * || See P. Potočnik, P. Spiga and G. Verret, ''Cubic vertex-transitive graphs on up to 1280 vertices''.
 |}
 </center>

@@ Line 57: / Line 57: @@
 |'''Color''' || style="text-align: center;" |'''Details'''
 |-
-|style="background-color: #eee; text-align: center;" | * || Cayley graphs; see the page for details.
+|style="background-color: #eee; text-align: center;" | * || Cayley graphs; see the [[The_Degree_Diameter_Problem_for_Cayley_Graphs | separate page]] for details.
 |-
 |style="background-color: #FF0066; text-align: center;" | * || Graphs found by Michael J. Dinneen and Paul Hafner. More details are available in a paper by the authors.