Maximum nullity of some Cayley graphs

Abstract

Abstract Recently, the nullity, the algebraic multiplicity of the number zero in the spectrum of the adjacency matrix, of a molecular graph has received a lot of attention as it has a number of direct applications in organic chemistry. In this regard, many researchers have been trying to find an upper or lower bound for the maximum nullity (minimum rank), (), for a graph . In this paper, using a well-known result, which presents the spectrum of a Cayley graph in terms of irreducible characters of the underlying group, and using representation and character of groups, we give a lower bound for the maximum nullity of Cayley graph, , where is a cyclic group, or such that is a cyclic group and is an arbitrary finite group, for , with determine the spectrum of Cayley graphs.