TempArcTransitive
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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. |