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