n | k | µ |
\lambda | t | exists ? | construction / proof of non-existence | no. of graphs |

6 | 2 | 1 | 0 | 1 | + | 1 | |

8 | 3 | 1 | 1 | 2 | + | 1 | |

10 | 4 | 2 | 1 | 2 | + | D6.1 | 16 |

12 | 3 | 1 | 0 | 1 | + | D8.3 | 1 |

12 | 4 | 2 | 0 | 2 | + | D7.1 + (6,2,1,0,1) | 1 |

12 | 5 | 2 | 2 | 3 | + | D7.2 + (6,2,1,0,1) | 20 |

14 | 5 | 2 | 1 | 4 | NO | KMMZ, k=t+1 | 0 |

14 | 6 | 3 | 2 | 3 | + | D6.1 | 16495 |

15 | 4 | 1 | 1 | 2 | + | Hammersley | 5 |

15 | 5 | 2 | 1 | 2 | + | J1 | 1292 |

16 | 6 | 3 | 1 | 3 | NO | FKM, rank 4 | 0 |

16 | 7 | 2 | 4 | 5 | + | D7.2 + (8,3,1,1,2) | 1 |

16 | 7 | 3 | 3 | 4 | + | FKM | |

18 | 4 | 1 | 0 | 3 | + | Duval | 1 |

18 | 5 | 1 | 2 | 3 | + | FKM: Cayley graph of S_3 x Z_3 | 2 |

18 | 6 | 3 | 0 | 3 | + | D7.1+(6,2,1,0,1) | 1 |

18 | 7 | 3 | 2 | 5 | + | FKM | |

18 | 8 | 3 | 4 | 5 | + | D7.2+(6,2,1,0,1) | |

18 | 8 | 4 | 3 | 4 | + | D6.1 | |

20 | 4 | 1 | 0 | 1 | + | D8.3 | 1 |

20 | 7 | 2 | 3 | 4 | + | KMMZ 8.2: flag algebra | |

20 | 8 | 4 | 2 | 4 | + | D7.1+(10,4,2,1,2) | |

20 | 9 | 4 | 4 | 5 | + | D7.2+(10,4,2,1,2) | |

21 | 6 | 2 | 1 | 2 | + | J3: cayley graph | |

21 | 8 | 3 | 3 | 4 | + | KMMZ, flag algebra of PG(2,2) | |

22 | 9 | 4 | 3 | 6 | ? ? | ||

22 | 10 | 5 | 4 | 5 | + | D6.1 | |

24 | 5 | 1 | 1 | 2 | + | J2: lambda=mu | |

24 | 6 | 2 | 0 | 2 | + | D7.1 + (12,3,1,0,1) | 1 |

24 | 7 | 2 | 2 | 3 | + | D7.2 + (12,3,1,0,1) | |

24 | 8 | 3 | 2 | 3 | + | J3: Cayley graph of S_4 | |

24 | 8 | 4 | 0 | 4 | + | D7.1+(6,2,1,0,1) | |

24 | 9 | 4 | 2 | 7 | + | J3: Cayley graph of S_4 | |

24 | 10 | 4 | 4 | 8 | + | J3: Cayley graph of S_4 | |

24 | 10 | 5 | 3 | 5 | ? ? | ||

24 | 11 | 3 | 7 | 8 | + | D7.2 + (8,3,1,1,2) | |

24 | 11 | 4 | 6 | 7 | + | D7.2 + (6,2,1,0,1) | |

24 | 11 | 5 | 5 | 6 | + | Hobart & Shaw | |

25 | 9 | 2 | 5 | 6 | NO | J3: Rank 4 | 0 |

25 | 10 | 6 | 1 | 6 | NO | J3: Rank 3 | 0 |

26 | 11 | 5 | 4 | 7 | + | J3: Aut-group Z_13 | |

26 | 12 | 6 | 5 | 6 | + | KMMZ: Cayley of dihedral group | |

A pdf of this paper.

Adjacency matrices of some of the dsrg's found in paper

Discrete Mathematics 264 (2003) 111-126.

Results on the exact number of non isomorphic graphs are mainly from J1 and J3.

J4

Se also: Mixed Moore graphs and other dsrg