On the nullity of connected graphs with least eigenvalue at least -2

Abstract

Let L (resp. L+) be the set of connected graphs with least adjacency eigenvalue at least -2 (resp. larger than -2). The nullity of a graph G, denoted by ?(G), is the multiplicity of zero as an eigenvalue of the adjacency matrix of G. In this paper, we give the nullity set of L+ and an upper bound on the nullity of exceptional graphs. An expression for the nullity of generalized line graphs is given. For G ? L, if ?(G) is sufficiently large, then G is a proper generalized line graph (G is not a line graph).