On graphs in which the neighborhood of each vertex is isomorphic to the Higman-Sims graph
Let \(\Gamma\) be a simple graph and \(a\) be a fixed vertex in \(\Gamma\). Let \(\Gamma_i(a)\) denote the \(i\)-neighborhood of \(a\), i.e., the subgraph induced by \(\Gamma\) on the set of all vertices that are at distance \(i\) from \(a\). \(\Gamma\) is called an amply regular graph with parameters \((v,k,\lambda,\mu)\) if \(\Gamma\) is a regular graph of degree \(k\) on \(v\) vertices in which each edge lies in \(\lambda\) triangles and \(\Gamma_1(a) \cup \Gamma_1(b)\) contains \(\mu\) vertices for any two vertices \(a\) and \(b\) separated by a distance of \(2\) in \(\Gamma\). An amply regular graph of distance \(2\) is called a strongly regular graph. A strongly regular graph with parameters \((100,22,0,6)\) is called Higman-Sims graph. In this work all connected amply regular graphs in which the neighborhoods of the vertices are isomorphic to the Higman-Sims graph are described.
scientific article; zbMATH DE number 5998440