The adjacency spectrum of two new operations of graphs

Abstract

Let G be a graph and A=A(G) be its adjacency matrix. The eigenvalues μ1,μ2,…,μn of A(G) are the eigenvalues of G and form the adjacency spectrum, denoted by Spec(G). In this paper, we introduce two new operations G1■k(G3□G2) and (G4□G1)■k(G3□G2), and describe the adjacency spectra of G1■k(G3□G2) and (G4□G1)■k(G3□G2) of regular graphs G1, G2 and arbitrarily graphs G3, G4 in terms of their adjacency spectra. As the applications, we obtain some new integral spectrum graphs.