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 | 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. |