On automorphisms of strongly regular graphs with parameters (99, 42, 21, 15) and (99, 56, 28, 36)

Abstract

We consider undirected graphs without loops or multiple edges. If a and b are vertices in a graph Γ, then d(a, b) denotes the distance between a and b, and Γi(a) denotes the subgraph of Γ induced by the set of vertices of Γ that are a distance of i away from a. The subgraph Γ1(a) is called the neighborhood of a and is denoted by [a]. By a ⊥ we denote the subgraph that is the ball of radius 1 centered at a. Γ is called a regular graph of degree k if [a] contains precisely k vertices for any vertex a in Γ. A graph Γ is – ≤