On the spectrum and energy of singular graphs

Abstract

Energy of a graph is defined as the sum of the absolute values of the eigenvalues of the adjacency matrix A(G) of a graph G and is denoted by E(G). The graph G with n vertices is called nonhypoenergetic if E(G)≥n and hypoenergetic if E(G)<n. Singular graphs are graphs with nullity η(G)>0. In this paper we study about nonhypoenergetic and hypoenergetic graphs among singular graphs. We also construct singular graphs of larger nullity using coalescence.