The three Chang graphs can be obtained by Seidel switching from T(8)
(the line graph of K_{8}). Namely, switch w.r.t. a set of edges
that induces the following subgraph of K_{8}:
(a) 4 pairwise disjoint edges,
(b) C_{3} + C_{5},
(c) an 8-cycle C_{8}.

name | group size | max cliques | max cocliques | clique cover | chromatic number |
---|---|---|---|---|---|

T(8) | 40320 | 3^{56},7^{8} |
4^{105} |
6 | 7 |

Chang1 | 384 | 4^{32},5^{24},6^{8} |
3^{128},4^{73} |
7 | 7 |

Chang2 | 360 | 4^{75},5^{30},6^{3} |
3^{160},4^{65} |
8 | 7 |

Chang3 | 96 | 4^{48},5^{48} |
3^{160},4^{65} |
6 | 7 |

References:

[1] L.C. Chang,
*The uniqueness and nonuniqueness of triangular association schemes*,
Sci. Record **3** (1959) 604-613.

[2] L.C. Chang,
*Association schemes of partially balanced block designs with parameters
v = 28, n _{1} = 12, n_{2} = 15 and
p_{11}^{2} = 4*,
Sci. Record