M22 graph

The M22 graph, also called the Mesner graph, is the unique strongly regular graph with parameters (77, 16, 0, 4). It is constructed from the Steiner system (3, 6, 22) by representing its 77 blocks as vertices and joining two vertices iff they have no terms in common or by deleting a vertex and its neighbors from the Higman–Sims graph.
It is one of seven known triangle-free strongly regular graphs. Its graph spectrum is (−6)21255161, and its automorphism group is the Mathieu group M22.