The adjacency spectrum of two new operations of graphs. Issue 3 (1st December 2018) - Wang, Dijian; Hou, Yaoping; Tang, Zikai
Abstract: Let G be a graph and A = A ( G ) be its adjacency matrix. The eigenvalues μ 1, μ 2, …, μ n of A ( G ) are the eigenvalues of G and form the adjacency spectrum, denoted by S p e c ( G ) . In this paper, we introduce two new operations G 1 ■ k ( G 3 □ G 2 ) and ( G 4 □ G 1 ) ■ k ( G 3 □ G 2 ), and describe the adjacency spectra of G 1 ■ k ( G 3 □ G 2 ) and ( G 4 □ G 1 ) ■ k ( G 3 □ G 2 ) of regular graphs G 1, G 2 and arbitrarily graphs G 3, G 4 in terms of their adjacency spectra. As the applications, we obtain some new integral spectrum graphs.