Shrikhande graph

This graph is the complement of the Latin square graph for the cyclic Latin square of order 4. The bipartite double is the folded 6-cube, with automorphism group of order 23040 = 25.6!. The folded 6-cube is also the bipartite double of the 4x4 lattice graph H(2,4). The graph that has the triangles of the Shrikhande graph as vertices, adjacent when they share an edge, is the Dyck graph . The complement of the Shrikhande graph has independence number 3 and chromatic number 6. For comparison, the other graph with the same parameters (called 4x4 or H(2,4) or L2(4)) has independence and chromatic number 4, like the Shrikhande graph, and also its complement has independence and chromatic number 4. Thus, the complement of the 4x4 grid graph and the complement of the Shrikhande graph are strongly regular graphs with the same parameters but different independence and chromatic number.