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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
3 999 999 999 999 999 999 999 999 999
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
3 999 999 999 999 999 999 999 999 999
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.