On K 1,3-free strictly Deza graphs

Abstract

A graph on v vertices is called a Deza graph with parameters (v, k, b, a) if it is k-regular and the number of common neighbors of two distinct vertices takes on one of two values. We describe strictly Deza graphs that do not contain K 1,3 among their induced subgraphs and are unions of closed neighborhoods of two nonadjacent vertices. The latter condition means that there are two nonadjacent vertices such that any other vertex is adjacent to at least one of the them.