On automorphisms of strongly regular locally cyclic graphs

Automorphisms of a distance-regular graph with intersection array is solved. Undirected graphs without loops or multiple edges have been considered. The degree of a vertex is defined as the number of vertices in its neighborhood. γ is called a regular graph of degree k if the degree of any vertex in γ is k. Given a subset X of automorphisms of γ, let Fix(X) denote the set of all vertices of γ that are fixed under any automorphism from X. The theorem is proved using Higman's method for handling automorphisms of a distance-regular graph. The graph γ is associated with a symmetric scheme of relations with d classes, where X is the vertex set of the graph, R 0 is the equality relation on X, and the class R i with i ≤ 1 consists of pairs (u, w).