Strongly regular graphs

This is just a list of strongly regular graph parameters for small numbers of vertices to replace the paper copy that I keep losing. At the moment it is nothing more than a list of the feasible parameter sets. However as time goes by and I stumble over these graphs or their constructions or whatever, I hope to fill in some of the blank fields left for that purpose.

If a number in the table is a link, then it will contain a copy of the actual graph in graph6 format.

If you want to know more about a specific parameter set (for any distance regular graph at all), then you should use the superb program DRG written by Andries Brouwer from the Discrete Mathematics group at the University of Eindhoven.

Table of Contents




Introduction

The paper Strongly regular graphs and partial geometries by Brouwer and van Lint, gives a simple introduction to the theory of strongly regular graphs.




Strongly regular graph parameters on 5-99 vertices

The fields in the following table are all straightforward. The parameters are given in the standard (n,k,a,c) fashion. The eigenvalues of the adjacency matrix are called theta and tau with respective multiplicities m_theta and m_tau .

The Number field (will eventually) give some indication of the number of graphs known, the Type field indicates if the graph is a conference graph or a Smith graph (one of the Krein conditions is tight). Any further comments will be linked into the final column.

Parameters theta m_theta tau m_tau Number Type Comments
(5, 2, 0, 1) 0.618 2 -1.618 2 ? Conf. none yet
(9, 4, 1, 2) 1.000 4 -2.000 4 ? Conf. none yet
(10, 3, 0, 1) 1 5 -2 4 ?   none yet
(13, 6, 2, 3) 1.303 6 -2.303 6 ? Conf. none yet
(15, 6, 1, 3) 1 9 -3 5 ?   none yet
(16, 5, 0, 2) 1 10 -3 5 ? Smith none yet
(16, 6, 2, 2) 2 6 -2 9 2!   Comp. OA(3,4)
(17, 8, 3, 4) 1.562 8 -2.562 8 ? Conf. none yet
(21, 10, 3, 6) 1 14 -4 6 ?   none yet
(21, 10, 5, 4) 3 6 -2 14 ?   none yet
(25, 8, 3, 2) 3 8 -2 16 ?   none yet
(25, 12, 5, 6) 2.000 12 -3.000 12 ? Conf. none yet
(26, 10, 3, 4) 2 13 -3 12 ?   none yet
(27, 10, 1, 5) 1 20 -5 6 ? Smith none yet
(28, 12, 6, 4) 4 7 -2 20 4 3 Chang + L(K_8) none yet
(29, 14, 6, 7) 2.193 14 -3.193 14 ? Conf. none yet
(35, 16, 6, 8) 2 20 -4 14 ?   none yet
(36, 10, 4, 2) 4 10 -2 25 ?   none yet
(36, 14, 4, 6) 2 21 -4 14 ?   none yet
(36, 14, 7, 4) 5 8 -2 27 ?   none yet
(36, 15, 6, 6) 3 15 -3 20 ?   none yet
(37, 18, 8, 9) 2.541 18 -3.541 18 ? Conf. none yet
(40, 12, 2, 4) 2 24 -4 15 ?   none yet
(41, 20, 9, 10) 2.702 20 -3.702 20 ? Conf. none yet
(45, 12, 3, 3) 3 20 -3 24 ?   none yet
(45, 16, 8, 4) 6 9 -2 35 ?   none yet
(45, 22, 10, 11) 2.854 22 -3.854 22 ? Conf. none yet
(49, 12, 5, 2) 5 12 -2 36 ?   none yet
(49, 16, 3, 6) 2 32 -5 16 ?   none yet
(49, 18, 7, 6) 4 18 -3 30 ?   none yet
(49, 24, 11, 12) 3.000 24 -4.000 24 ? Conf. none yet
(50, 7, 0, 1) 2 28 -3 21 1!   Hoffman-Singleton
(50, 21, 8, 9) 3 25 -4 24 ?   none yet
(53, 26, 12, 13) 3.140 26 -4.140 26 ? Conf. none yet
(55, 18, 9, 4) 7 10 -2 44 ?   none yet
(56, 10, 0, 2) 2 35 -4 20 ?   none yet
(57, 14, 1, 4) 2 38 -5 18 ?   none yet
(57, 24, 11, 9) 5 18 -3 38 ?   none yet
(61, 30, 14, 15) 3.405 30 -4.405 30 ? Conf. none yet
(63, 30, 13, 15) 3 35 -5 27 ?   none yet
(64, 14, 6, 2) 6 14 -2 49 ?   none yet
(64, 18, 2, 6) 2 45 -6 18 ?   none yet
(64, 21, 8, 6) 5 21 -3 42 ?   none yet
(64, 27, 10, 12) 3 36 -5 27 ?   none yet
(64, 28, 12, 12) 4 28 -4 35 ?   none yet
(65, 32, 15, 16) 3.531 32 -4.531 32 ? Conf. none yet
(66, 20, 10, 4) 8 11 -2 54 ?   none yet
(69, 20, 7, 5) 5 23 -3 45 ?   none yet
(70, 27, 12, 9) 6 20 -3 49 ?   none yet
(73, 36, 17, 18) 3.772 36 -4.772 36 ? Conf. none yet
(75, 32, 10, 16) 2 56 -8 18 ?   none yet
(76, 21, 2, 7) 2 56 -7 19 ?   none yet
(76, 30, 8, 14) 2 57 -8 18 ?   none yet
(76, 35, 18, 14) 7 19 -3 56 ?   none yet
(77, 16, 0, 4) 2 55 -6 21 ?   none yet
(78, 22, 11, 4) 9 12 -2 65 ?   none yet
(81, 16, 7, 2) 7 16 -2 64 ?   none yet
(81, 20, 1, 6) 2 60 -7 20 ?   none yet
(81, 24, 9, 6) 6 24 -3 56 ?   none yet
(81, 30, 9, 12) 3 50 -6 30 ?   none yet
(81, 32, 13, 12) 5 32 -4 48 ?   none yet
(81, 40, 19, 20) 4.000 40 -5.000 40 ? Conf. none yet
(82, 36, 15, 16) 4 41 -5 40 ?   none yet
(85, 14, 3, 2) 4 34 -3 50 ?   none yet
(85, 20, 3, 5) 3 50 -5 34 ?   none yet
(85, 30, 11, 10) 5 34 -4 50 ?   none yet
(85, 42, 20, 21) 4.110 42 -5.110 42 ? Conf. none yet
(88, 27, 6, 9) 3 55 -6 32 ?   none yet
(89, 44, 21, 22) 4.217 44 -5.217 44 ? Conf. none yet
(91, 24, 12, 4) 10 13 -2 77 ?   none yet
(95, 40, 12, 20) 2 75 -10 19 ?   none yet
(96, 19, 2, 4) 3 57 -5 38 ?   none yet
(96, 20, 4, 4) 4 45 -4 50 ?   none yet
(96, 35, 10, 14) 3 63 -7 32 ?   none yet
(96, 38, 10, 18) 2 76 -10 19 ?   none yet
(96, 45, 24, 18) 9 20 -3 75 ?   none yet
(97, 48, 23, 24) 4.424 48 -5.424 48 ? Conf. none yet
(99, 14, 1, 2) 3 54 -4 44 ?   none yet
(99, 42, 21, 15) 9 21 -3 77 ?   none yet
(99, 48, 22, 24) 4 54 -6 44 ?   none yet


[Home], Gordon Royle, gordon@cs.uwa.edu.au, August 1996