On automorphisms of strongly regular graphs with $\lambda=0$ and $\mu=3$

Abstract

Abstract. A strongly regular graph with λ = 0 and μ = 3 is of degree 3 or 21. The automorphisms of prime order and the subgraphs of their fixed points are described for a strongly regular graph Γ with parameters (162, 21, 0, 3). In particular, the inequality |G/O(G)| ≤ 2 holds true for G = Aut(Γ).

On a family of strongly regular graphs withλ=1

“…However, Higman proved that the automorphism group of such a graph could not be even vertex transitive, see, for example, [5]. Later, Higman's approach was widely generalized and applied for other graphs, see, e.g., [6] and [7]. The typical result is that, if for a given parameter set (v, k, λ, µ) a strongly regular graph exists, then it has a small automorphism group.…”