M22 graph
The M22 graph, also called the Mesner graph or Witt graph, is the unique strongly [regular graph] with parameters. It is constructed from the Steiner system 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.
For any term, the family of blocks that contain that term forms an independent set in this graph, with 21 vertices. In a result analogous to the Erdős–Ko–Rado theorem, these are the unique maximum independent sets in this graph.
It is one of seven known triangle-free strongly regular graphs. Its graph spectrum is 21255161, and its automorphism group is the Mathieu group M22.