Automorphisms of a Strongly Regular Graph with Parameters (1305, 440, 115, 165)

Abstract

A graph Γ is called t-isoregular if, for any i ≤ t and any i-vertex subset S, the number Γ(S) depends only on the isomorphism class of the subgraph induced by S. A graph Γ on v vertices is called absolutely isoregular if it is (v — 1)-isoregular. It is known that each 5-isoregular graph is absolutely isoregular, and such graphs have been fully described. Each precisely 4-isoregular graph is either a pseudogeometric graph for pG_r(2r, 2r³ + 3r² — 1) or its complement. A pseudogeometric graph for pG_r(2r, 2r³ + 3r² — 1) is denoted by Izo(r). Graphs Izo(r) do not exist for an infinite set of values of r (r = 3, 4, 6, 10,…). The existence of Izo(5) is unknown. In this work, we find possible automorphisms for the neighborhood of an edge from Izo(5).