Difference between revisions of "TempArcTransitive"
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| '''<math>d</math>\<math>k</math>'''|| '''2''' || '''3''' || '''4'''|| '''5''' || '''6''' || '''7''' || '''8''' || '''9''' || '''10''' | | '''<math>d</math>\<math>k</math>'''|| '''2''' || '''3''' || '''4'''|| '''5''' || '''6''' || '''7''' || '''8''' || '''9''' || '''10''' | ||
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| − | | '''3''' || style="background-color: #eee;" | | + | | '''3''' || style="background-color: #eee;" | '''10''' || style="background-color: #eee;" | '''14''' || style="background-color: #eee;" | '''30''' ||style="background-color: #eee;" | '''60''' || style="background-color: #eee;" | '''64''' ||style="background-color: #eee;" | '''168''' ||style="background-color: #eee;" | '''234''' ||style="background-color: #eee;" | '''364''' ||style="background-color: #eee;" | '''1250''' |
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| '''4''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 | | '''4''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 | ||
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| '''<math>d</math>\<math>k</math>'''|| '''2''' || '''3''' || '''4'''|| '''5''' || '''6''' || '''7''' || '''8''' || '''9''' || '''10''' | | '''<math>d</math>\<math>k</math>'''|| '''2''' || '''3''' || '''4'''|| '''5''' || '''6''' || '''7''' || '''8''' || '''9''' || '''10''' | ||
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| − | | '''3''' || style="background-color: #eee;" | | + | | '''3''' || style="background-color: #eee;" | 6 || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - |
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| − | | '''4''' || style="background-color: #eee;" | | + | | '''4''' || style="background-color: #eee;" | 13 || style="background-color: #eee;" | 25 || style="background-color: #eee;" | 41 ||style="background-color: #eee;" | 61 || style="background-color: #eee;" | 85 ||style="background-color: #eee;" | 113 ||style="background-color: #eee;" | 145 ||style="background-color: #eee;" | 181 ||style="background-color: #eee;" | 221 |
|- | |- | ||
| − | | '''5''' || style="background-color: #eee;" | | + | | '''5''' || style="background-color: #eee;" | 10 || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - |
|- | |- | ||
| − | | '''6''' || style="background-color: #eee;" | | + | | '''6''' || style="background-color: #eee;" | 19 || style="background-color: #eee;" | 38 || style="background-color: #eee;" | 117 ||style="background-color: #eee;" | 171 || style="background-color: #eee;" | 279 ||style="background-color: #eee;" | 515 ||style="background-color: #eee;" | 695 ||style="background-color: #eee;" | 905 ||style="background-color: #eee;" | 1393 |
|- | |- | ||
| − | | '''7''' || style="background-color: #eee;" | | + | | '''7''' || style="background-color: #eee;" | 14 || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - |
|- | |- | ||
| − | | '''8''' || style="background-color: #eee;" | | + | | '''8''' || style="background-color: #eee;" | 17 || style="background-color: #eee;" | 75 || style="background-color: #eee;" | 146 ||style="background-color: #eee;" | 401 || style="background-color: #eee;" | 777 ||style="background-color: #eee;" | 1365 ||style="background-color: #eee;" | 2129 ||style="background-color: #eee;" | 3281 ||style="background-color: #eee;" | 5081 |
|- | |- | ||
| − | | '''9''' || style="background-color: #eee;" | | + | | '''9''' || style="background-color: #eee;" | 18 || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - |
|- | |- | ||
| − | | '''10''' || style="background-color: #eee;" | | + | | '''10''' || style="background-color: #eee;" | 41 || style="background-color: #eee;" | 151 || style="background-color: #eee;" | 363 ||style="background-color: #eee;" | 1023 || style="background-color: #eee;" | 1623 ||style="background-color: #eee;" | 4443 ||style="background-color: #eee;" | 6663 ||style="background-color: #eee;" | 11163 ||style="background-color: #eee;" | 18483 |
|- | |- | ||
| − | | '''11''' || style="background-color: #eee;" | | + | | '''11''' || style="background-color: #eee;" | 22 || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - |
|- | |- | ||
| − | | '''12''' || style="background-color: #eee;" | | + | | '''12''' || style="background-color: #eee;" | 57 || style="background-color: #eee;" | 185 || style="background-color: #eee;" | 785 ||style="background-color: #eee;" | 1685 || style="background-color: #eee;" | 3965 ||style="background-color: #eee;" | 10777 ||style="background-color: #eee;" | 15769 ||style="background-color: #eee;" | 35269 ||style="background-color: #eee;" | 52429 |
|- | |- | ||
| − | | '''13''' || style="background-color: #eee;" | | + | | '''13''' || style="background-color: #eee;" | 26 || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - |
|- | |- | ||
| − | | '''14''' || style="background-color: #eee;" | | + | | '''14''' || style="background-color: #eee;" | 71 || style="background-color: #eee;" | 379 || style="background-color: #eee;" | 953 ||style="background-color: #eee;" | 3067 || style="background-color: #eee;" | 8023 ||style="background-color: #eee;" | 18415 ||style="background-color: #eee;" | 37803 ||style="background-color: #eee;" | 72327 ||style="background-color: #eee;" | 196689 |
|- | |- | ||
| − | | '''15''' || style="background-color: #eee;" | | + | | '''15''' || style="background-color: #eee;" | 30 || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - |
|- | |- | ||
| − | | '''16''' || style="background-color: #eee;" | | + | | '''16''' || style="background-color: #eee;" | 97 || style="background-color: #eee;" | 401 || style="background-color: #eee;" | 1649 ||style="background-color: #eee;" | 4947 || style="background-color: #eee;" | 14081 ||style="background-color: #eee;" | 35921 ||style="background-color: #eee;" | 80257 ||style="background-color: #eee;" | 173969 ||style="background-color: #eee;" | 354433 |
|- | |- | ||
| − | | '''17''' || style="background-color: #eee;" | | + | | '''17''' || style="background-color: #eee;" | 34 || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - |
|- | |- | ||
| − | | '''18''' || style="background-color: #eee;" | | + | | '''18''' || style="background-color: #eee;" | ? || style="background-color: #eee;" | ? || style="background-color: #eee;" | 1393 ||style="background-color: #eee;" | ? || style="background-color: #eee;" | ? ||style="background-color: #eee;" | ? ||style="background-color: #eee;" | ? ||style="background-color: #eee;" | ? ||style="background-color: #eee;" | ? |
|- | |- | ||
| − | | '''19''' || style="background-color: #eee;" | | + | | '''19''' || style="background-color: #eee;" | 38 || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - |
|- | |- | ||
| − | | '''20''' || style="background-color: #eee;" | | + | | '''20''' || style="background-color: #eee;" | 101 || style="background-color: #eee;" | ? || style="background-color: #eee;" | ? ||style="background-color: #eee;" | ? || style="background-color: #eee;" | ? ||style="background-color: #eee;" | 106025 ||style="background-color: #eee;" | ? ||style="background-color: #eee;" | ? ||style="background-color: #eee;" | ? |
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|} | |} | ||
Latest revision as of 17:49, 2 October 2024
NB This page is incomplete and still under construction.
Table of the orders of the largest known arc-transitive graphs for the undirected degree diameter problem
Below is the table of the largest known arc-transitive graphs in the undirected degree diameter problem for graphs of degree 3 ≤ d ≤ 20 and diameter 2 ≤ k ≤ 10. All graphs which are known to be optimal are marked in bold.
| [math]d[/math]\[math]k[/math] | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 3 | 10 | 14 | 30 | 60 | 64 | 168 | 234 | 364 | 1250 |
| 4 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 5 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 6 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 7 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 8 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 9 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 10 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 11 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 12 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 13 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 14 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 15 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 16 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 17 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 18 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 19 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
| 20 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 | 999 |
The following table is the key to the colors in the table presented above:
| Color | Details |
| * | Details. |
Table of the orders of the largest known arc-transitive circulant graphs for the undirected degree diameter problem
Below is the table of the largest known arc-transitive circulant graphs in the undirected degree diameter problem for graphs of degree 3 ≤ d ≤ 20 and diameter 2 ≤ k ≤ 10. All graphs which are known to be optimal are marked in bold.
| [math]d[/math]\[math]k[/math] | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 3 | 6 | - | - | - | - | - | - | - | - |
| 4 | 13 | 25 | 41 | 61 | 85 | 113 | 145 | 181 | 221 |
| 5 | 10 | - | - | - | - | - | - | - | - |
| 6 | 19 | 38 | 117 | 171 | 279 | 515 | 695 | 905 | 1393 |
| 7 | 14 | - | - | - | - | - | - | - | - |
| 8 | 17 | 75 | 146 | 401 | 777 | 1365 | 2129 | 3281 | 5081 |
| 9 | 18 | - | - | - | - | - | - | - | - |
| 10 | 41 | 151 | 363 | 1023 | 1623 | 4443 | 6663 | 11163 | 18483 |
| 11 | 22 | - | - | - | - | - | - | - | - |
| 12 | 57 | 185 | 785 | 1685 | 3965 | 10777 | 15769 | 35269 | 52429 |
| 13 | 26 | - | - | - | - | - | - | - | - |
| 14 | 71 | 379 | 953 | 3067 | 8023 | 18415 | 37803 | 72327 | 196689 |
| 15 | 30 | - | - | - | - | - | - | - | - |
| 16 | 97 | 401 | 1649 | 4947 | 14081 | 35921 | 80257 | 173969 | 354433 |
| 17 | 34 | - | - | - | - | - | - | - | - |
| 18 | ? | ? | 1393 | ? | ? | ? | ? | ? | ? |
| 19 | 38 | - | - | - | - | - | - | - | - |
| 20 | 101 | ? | ? | ? | ? | 106025 | ? | ? | ? |
The following table is the key to the colors in the table presented above:
| Color | Details |
| * | Details. |