On the automorphisms of the strongly regular graph with parameters (85, 14, 3, 2)

Abstract

Let Γ be the strongly regular graph with parameters (85, 14, 3, 2), g be an element of prime order p of Aut(Γ) and Δ = Fix(g). In this paper, it is proved that either p = 5 or p = 17 and Δ is the empty graph, or p = 7 and Δ is a 1-clique, or p = 5 and Δ is a 5-clique, or p = 3 and Δ is a quadrangle or a 2 x lattice, or p = 2 and Δ is a union of φ isolated vertices and ψ isolated triangles, ψ = 1 and φ ∈ {4, 6} or ψ = 0 and φ = 5. In addition, it is shown that the graph Γ is not vertex transitive. © de Gruyter 2009.