Table of vertex-symmetric digraphs explained

The best known vertex transitive digraphs (as of October 2008) in the directed Degree diameter problem are tabulated below.

Table of the orders of the largest known vertex-symmetric graphs for the directed degree diameter problem

	2	3	4	5	6	7	8	9	10	11
2	6^[1]	10^[2]	20^[3]	27	72^[4]	144	171	336^[5]	504	737
3	12	27	60^[6]	165^[7]	333	1 152^[8]	2 041^[9]	5 115	11 568	41 472
4	20	60	168	465	1 378	7 200	14 400^[10]	42 309	137 370	648 000
5	30	120	360	1 152	3 775	28 800	86 400	259 200	1 010 658	5 184 000
6	42	210	840	2 520	9 020	88 200	352 800	1 411 200	5 184 000	27 783 000
7	56	336	1 680	6 720	20 160	225 792	1 128 960	5 644 800	27 783 000	113 799 168
8	72	504	3 024	15 120	60 480	508 032	3 048 192	18 289 152	113 799 168	457 228 800
9	90	720	5 040	30 240	151 200	1 036 800	7 257 600	50 803 200	384 072 192	1 828 915 200
10	110	990	7 920	55 400	332 640	1 960 200	15 681 600	125 452 800	1 119 744 000	6 138 320 000
11	132	1 320	11 880	95 040	665 280	3 991 680	31 152 000	282 268 800	2 910 897 000	18 065 203 200
12	156	1 716	17 160	154 440	1 235 520	8 648 640	58 893 120	588 931 200	6 899 904 000	47 703 427 200
13	182	2 184	24 024	240 240	2 162 160	17 297 280	121 080 960	1 154 305 152	15 159 089 098	115 430 515 200

The footnotes in the table indicate the origin of the digraph that achieves the given number of vertices:

External links

• Vertex-symmetric Digraphs online table.
• The Degree - Diameter Problem on CombinatoricsWiki.org.
• Eyal Loz's Degree-Diameter problem page.

Notes and References

1. Family of digraphs found by .
2. Cayley digraphs found by Michael J. Dinneen. Details about these graphs are available in a paper by the author.
3. Cayley digraphs found by Michael J. Dinneen. The complete set of Cayley digraphs in that order was found by Eyal Loz.
4. Cayley digraphs found by Paul Hafner. Details about these graphs are available in a paper by the author.
5. Family of digraphs found by .
6. Digraph found by . The complete set of Cayley digraphs in that order was found by Eyal Loz.
7. Cayley digraph found by Paul Hafner. The complete set of Cayley digraphs in that order was found by Eyal Loz.
8. Digraphs found by .
9. Cayley digraphs found by Eyal Loz. More details are available in .
10. Digraphs found by J. Gómez.