Temp VertexTransitive

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Table of the orders of the largest known vertex-transitive graphs for the undirected degree diameter problem

Below is the table of the largest known vertex-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	82	168	300	546	1 250
4	13	35	84	273	513	1 155	3 080	7 550	17 604
5	18	60	210	546	1 640	5 500	16 965	57 840	187 056
6	32	108	375	1 395	5 115	19 383	76 461	307 845	1 253 615
7	50	168	672	2 756	11 988	52 768	249 660	1 223 050	6 007 230
8	48	253	1 100	5 060	23 991	131 137	734 820	4 243 100	24 897 161
9	60	294	1 550	8 200	45 612	279 616	1 686 600	12 123 288	65 866 350
10	72	406	2 286	13 140	81 235	583 083	4 293 452	27 997 191	201 038 922
11	84	486	2 860	19 500	139 446	1 001 268	7 442 328	72 933 102	500 605 110
12	96	605	3 775	29 470	229 087	1 999 500	15 924 326	158 158 875	1 225 374 192
13	162	680	4 788	40 260	347 126	3 322 080	29 927 790	233 660 788	2 129 329 324
14	128	873	6 510	57 837	530 448	5 600 532	50 128 239	579 328 377	7 041 746 081
15	144	972	7 956	76 518	787 116	8 599 986	88 256 520	1 005 263 436	10 012 349 898
16	200	1 155	9 576	100 650	1 125 264	12 500 082	135 340 551	1 995 790 371	12 951 451 931
17	200	1 260	12 090	133 144	1 609 830	18 495 162	220 990 700	3 372 648 954
18	200	1 510	15 026	171 828	2 193 321	26 515 120	323 037 476	5 768 971 167
19	338	1 638	17 658	221 676	3 030 544	39 123 116	501 001 000	8 855 580 344
20	210	1 958	21 333	281 820	4 040 218	55 625 185	762 374 779	12 951 451 931

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

Color	Details
*	Cayley graphs; see the separate page for details.
*	The Petersen graph.
*	See P. Potočnik, P. Spiga and G. Verret, Cubic vertex-transitive graphs on up to 1280 vertices.
*	The Hoffman-Singleton graph.
*	See B. D. McKay, M. Miller and J. Širáň, A note on large graphs of diameter two and given maximum degree.
*	See P. Potočnik, P. Spiga and G. Verret, Bounding the order of the vertex-stabiliser in 3-valent vertex transitive and 4-valent arc-transitive graphs.