The adjacency spectrum of two new operations of graphs. Issue 3 (1st December 2018)

• Record Type: Journal Article
• Authors: Wang, Dijian; Hou, Yaoping; Tang, Zikai
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 15:Issue 3(2018)
• Page Start: 284
• Page End: 290
• Publication Date: 2018-12-01
• Subjects: Adjacency spectrum -- Cartesian product(of graphs) -- Integral graphs
• DOI: 10.1016/j.akcej.2017.10.004
• Languages: English
• ISSNs: 0972-8600

Abstract

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.