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.