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 |
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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 |
| _version_ | 1811336983362928640 |
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| author | Dijian Wang Yaoping Hou Zikai Tang |
| author_facet | Dijian Wang Yaoping Hou Zikai Tang |
| author_sort | Dijian Wang |
| collection | DOAJ |
| description | 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 |
| first_indexed | 2024-04-13T17:47:28Z |
| format | Article |
| id | doaj.art-ef410ce09b2f4fb8895c8d8e092bcaf5 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 |
| language | English |
| last_indexed | 2024-04-13T17:47:28Z |
| publishDate | 2018-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-ef410ce09b2f4fb8895c8d8e092bcaf52022-12-22T02:36:53ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002018-12-01153284290The adjacency spectrum of two new operations of graphsDijian Wang0Yaoping Hou1Zikai Tang2Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, PR ChinaKey Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, PR ChinaCorresponding author.; Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, PR ChinaLet 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 graphshttp://www.sciencedirect.com/science/article/pii/S0972860017301706 |
| spellingShingle | Dijian Wang Yaoping Hou Zikai Tang The adjacency spectrum of two new operations of graphs AKCE International Journal of Graphs and Combinatorics |
| title | The adjacency spectrum of two new operations of graphs |
| title_full | The adjacency spectrum of two new operations of graphs |
| title_fullStr | The adjacency spectrum of two new operations of graphs |
| title_full_unstemmed | The adjacency spectrum of two new operations of graphs |
| title_short | The adjacency spectrum of two new operations of graphs |
| title_sort | adjacency spectrum of two new operations of graphs |
| url | http://www.sciencedirect.com/science/article/pii/S0972860017301706 |
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