On Strongly Regular Graphs with k=2μ and Their Extensions

Abstract

We obtain a convenient expression for the parameters of a strongly regular graph with k=2μ in terms of the nonprincipal eigenvalues x and −y. It turns out in particular that such graphs are pseudogeometric for pGx(2x,y−1). We prove that a strongly regular graph with parameters (35,16,6,8) is a quotient of the Johnson graph \(\bar J\)(8,4). We also find the parameters of strongly regular graphs in which the neighborhoods of vertices are pseudogeometric graphs for pGx(2x,t),x≤3. In consequence, we establish that a connected graph in which the neighborhoods of vertices are pseudogeometric graphs for pG3(6,2) is isomorphic to the Taylor graph on 72 vertices or to the alternating form graph Alt(4,2) with parameters (64,35,18,20).