The adjacency spectrum of two new operations of graphs
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2018-12-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0972860017301706 |
| Summary: | 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. Keywords: Adjacency spectrum, Cartesian product(of graphs), Integral graphs |
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| ISSN: | 0972-8600 |