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	-	-	-	-	-	-	-	-	-
4	13	25	41	61	85	113	145	181	221
5	-	-	-	-	-	-	-	-	-
6	19	38	117	171	279	515	695	905	1393
7	-	-	-	-	-	-	-	-	-
8	17	75	146	401	777	1365	2129	3281	5081
9	-	-	-	-	-	-	-	-	-
10	41	151	363	1023	1623	4443	6663	11163	18483
11	-	-	-	-	-	-	-	-	-
12	57	185	785	1685	3965	10777	1769?	35269	52429
13	-	-	-	-	-	-	-	-	-
14	71	379	953	3067	8023	18415	37803	72327	196689
15	-	-	-	-	-	-	-	-	-
16	97	401	1649	4947	14081	35921	80257	173969	354433
17	-	-	-	-	-	-	-	-	-
18	?	?	1393	?	?	?	?	?	?
19	-	-	-	-	-	-	-	-	-
20	101	?	?	?	?	106025	?	?	?

The following table is the key to the colors in the table presented above:

Color	Details
*	Details.