v | k | λ | μ | rf | sg | comments | |
---|---|---|---|---|---|---|---|
! | 5 | 2 | 0 | 1 | 0.6182 | –1.6182 | pentagon; Paley(5); Seidel 2-graph\* |
! | 9 | 4 | 1 | 2 | 14 | –24 | Paley(9); 32; 2-graph\* |
! | 10 | 3 | 0 | 1 | 15 | –24 | Petersen graph; NO–(4,2); NO–,orth(3,5); switch OA(3,2)+*; 2-graph |
6 | 3 | 4 | 14 | –25 | Triangular graph T(5); 2-graph | ||
! | 13 | 6 | 2 | 3 | 1.3036 | –2.3036 | Paley(13); 2-graph\* |
! | 15 | 6 | 1 | 3 | 19 | –35 | O(5,2) Sp(4,2); NO–(4,3); GQ(2,2); 2-graph\* |
8 | 4 | 4 | 25 | –29 | Triangular graph T(6); 2-graph\* | ||
! | 16 | 5 | 0 | 2 | 110 | –35 | q222=0; VO–(4,2) affine polar graph; projective binary [5,4] code with weights 2, 4; RSHCD–; 2-graph |
10 | 6 | 6 | 25 | –210 | Clebsch graph; q111=0; from 2-(4,2,1) with 1-factor Fickus et al.; 2-graph | ||
2! | 16 | 6 | 2 | 2 | 26 | –29 | Shrikhande graph; 42; Wallis (AR(2,1)+S(2,2,4)); from a partial spread: projective binary [6,4] code with weights 2, 4; RSHCD+; 2-graph |
9 | 4 | 6 | 19 | –36 | OA(4,3); Bilin2x2(2); Wallis2 (AR(2,1)+S(2,2,4)); Goethals-Seidel(2,3); VO+(4,2) affine polar graph; 2-graph | ||
! | 17 | 8 | 3 | 4 | 1.5628 | –2.5628 | Paley(17); 2-graph\* |
! | 21 | 10 | 3 | 6 | 114 | –46 | |
10 | 5 | 4 | 36 | –214 | Triangular graph T(7) | ||
- | 21 | 10 | 4 | 5 | 1.79110 | –2.79110 | Conf |
! | 25 | 8 | 3 | 2 | 38 | –216 | 52 |
16 | 9 | 12 | 116 | –48 | OA(5,4) | ||
15! | 25 | 12 | 5 | 6 | 212 | –312 | Paulus and Rozenfel'd; Paley(25); OA(5,3); 2-graph\* |
10! | 26 | 10 | 3 | 4 | 213 | –312 | Paulus and Rozenfel'd; switch OA(5,3)+*; 2-graph |
15 | 8 | 9 | 212 | –313 | S(2,3,13); 2-graph | ||
! | 27 | 10 | 1 | 5 | 120 | –56 | q222=0; O–(6,2) polar graph; Godsil(q=3,r=2); GQ(2,4); 2-graph\* |
16 | 10 | 8 | 46 | –220 | Schläfli graph; unique by Seidel; q111=0; 2-graph\* | ||
- | 28 | 9 | 0 | 4 | 121 | –56 | Krein2; Absolute bound |
18 | 12 | 10 | 46 | –221 | Krein1; Absolute bound | ||
4! | 28 | 12 | 6 | 4 | 47 | –220 | Chang graphs; Triangular graph T(8); Wallis (AR(2,1)+S(2,3,7)); 2-graph |
15 | 6 | 10 | 120 | –57 | NO+(6,2); Goethals-Seidel(3,3); pg(3,4,2) does not exist (De Clerck); Taylor 2-graph for U3(3) | ||
41! | 29 | 14 | 6 | 7 | 2.19314 | –3.19314 | complete enumeration by Bussemaker & Spence; Paley(29); 2-graph\* |
- | 33 | 16 | 7 | 8 | 2.37216 | –3.37216 | Conf |
3854! | 35 | 16 | 6 | 8 | 220 | –414 | complete enumeration by McKay & Spence; pg(4,3,2) does not exist (De Clerck); 2-graph\* |
18 | 9 | 9 | 314 | –320 | S(2,3,15); lines in PG(3,2); O+(6,2); from ETF Fickus et al.; 2-graph\* | ||
! | 36 | 10 | 4 | 2 | 410 | –225 | 62 |
25 | 16 | 20 | 125 | –510 | OA(6,5) does not exist (Tarry) | ||
180! | 36 | 14 | 4 | 6 | 221 | –414 | U3(3).2 / L2(7).2 - subconstituent of Hall-Janko graph; complete enumeration by McKay & Spence; RSHCD–; 2-graph |
21 | 12 | 12 | 314 | –321 | 2-graph | ||
! | 36 | 14 | 7 | 4 | 58 | –227 | Triangular graph T(9) |
21 | 10 | 15 | 127 | –68 | |||
32548! | 36 | 15 | 6 | 6 | 315 | –320 | complete enumeration by McKay & Spence; OA(6,3); NO–(6,2); RSHCD+; 2-graph |
20 | 10 | 12 | 220 | –415 | NO–(5,3); OA(6,4) does not exist (Tarry); 2-graph | ||
+ | 37 | 18 | 8 | 9 | 2.54118 | –3.54118 | partial enumeration by McKay & Spence; see also Crnković-Maksimović and Maksimović-Rukavina; Paley(37); 2-graph\* |
28! | 40 | 12 | 2 | 4 | 224 | –415 | complete enumeration by Spence; O(5,3) Sp(4,3); GQ(3,3) |
27 | 18 | 18 | 315 | –324 | NU(4,2) | ||
+ | 41 | 20 | 9 | 10 | 2.70220 | –3.70220 | Maksimović-Rukavina; Paley(41); 2-graph\* |
78! | 45 | 12 | 3 | 3 | 320 | –324 | complete enumeration by Coolsaet, Degraer & Spence; U(4,2) polar graph; Wallis (AR(3,1)+S(2,2,5)); GQ(4,2) |
32 | 22 | 24 | 224 | –420 | NO+(5,3) | ||
! | 45 | 16 | 8 | 4 | 69 | –235 | Triangular graph T(10) |
28 | 15 | 21 | 135 | –79 | pg(4,6,3) | ||
+ | 45 | 22 | 10 | 11 | 2.85422 | –3.85422 | Mathon; 2-graph\* |
! | 49 | 12 | 5 | 2 | 512 | –236 | 72 |
36 | 25 | 30 | 136 | –612 | OA(7,6) | ||
- | 49 | 16 | 3 | 6 | 232 | –516 | Bussemaker-Haemers-Mathon-Wilbrink |
32 | 21 | 20 | 416 | –332 | |||
+ | 49 | 18 | 7 | 6 | 418 | –330 | Behbahani-Lam; Crnković-Maksimović; OA(7,3); Pasechnik(7) |
30 | 17 | 20 | 230 | –518 | OA(7,5) | ||
+ | 49 | 24 | 11 | 12 | 324 | –424 | Paley(49); OA(7,4); 2-graph\* |
! | 50 | 7 | 0 | 1 | 228 | –321 | U3(52).2 / Sym(7) - Hoffman-Singleton |
42 | 35 | 36 | 221 | –328 | |||
- | 50 | 21 | 4 | 12 | 142 | –97 | Absolute bound |
28 | 18 | 12 | 87 | –242 | Absolute bound | ||
+ | 50 | 21 | 8 | 9 | 325 | –424 | switch OA(7,4)+*; switch skewhad2+*; 2-graph |
28 | 15 | 16 | 324 | –425 | S(2,4,25); 2-graph |