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Chang graphs

Chang proved that the triangular graphs T(n) are uniquely determined by their parameters (as strongly regular graph), with the exception of T(8). Furthermore, that there are up to isomorphism precisely four strongly regular graphs with parameters v = 28, k = 12, λ = 6, μ =4, namely T(8) and three other graphs, known as the Chang graphs.

The three Chang graphs can be obtained by Seidel switching from T(8) (the line graph of K8). Namely, switch w.r.t. a set of edges that induces the following subgraph of K8: (a) 4 pairwise disjoint edges, (b) C3 + C5, (c) an 8-cycle C8.

name group size max cliques max cocliques clique cover chromatic number
T(8) 40320 356,78 4105 6 7
Chang1 384 432,524,68 3128,473 7 7
Chang2 360 475,530,63 3160,465 8 7
Chang3 96 448,548 3160,465 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, n1 = 12, n2 = 15 and p112 = 4, Sci. Record 4 (1960) 12-18.