TempArcTransitive

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.