Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum
Let Γ=V,E be a graph. If all the eigenvalues of the adjacency matrix of the graph Γ are integers, then we say that Γ is an integral graph. A graph Γ is determined by its spectrum if every graph cospectral to it is in fact isomorphic to it. In this paper, we investigate some algebraic properties of t...
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2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6632206 |
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| author | Jia-Bao Liu S. Morteza Mirafzal Ali Zafari |
| author_facet | Jia-Bao Liu S. Morteza Mirafzal Ali Zafari |
| author_sort | Jia-Bao Liu |
| collection | DOAJ |
| description | Let Γ=V,E be a graph. If all the eigenvalues of the adjacency matrix of the graph Γ are integers, then we say that Γ is an integral graph. A graph Γ is determined by its spectrum if every graph cospectral to it is in fact isomorphic to it. In this paper, we investigate some algebraic properties of the Cayley graph Γ=Cayℤn,S, where n=pm (p is a prime integer and m∈ℕ) and S=a∈ℤn|a,n=1. First, we show that Γ is an integral graph. Also, we determine the automorphism group of Γ. Moreover, we show that Γ and Kv▽Γ are determined by their spectrum. |
| format | Article |
| id | doaj-art-178af0d999bc44f68912e00f02aeb21c |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-178af0d999bc44f68912e00f02aeb21c2025-02-03T06:46:22ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66322066632206Some Algebraic Properties of a Class of Integral Graphs Determined by Their SpectrumJia-Bao Liu0S. Morteza Mirafzal1Ali Zafari2School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaLorestan University, Department of Mathematics, Faculty of Science, Khorramabad, IranDepartment of Mathematics, Faculty of Science, Payame Noor University, P.O. Box 19395-4697, Tehran, IranLet Γ=V,E be a graph. If all the eigenvalues of the adjacency matrix of the graph Γ are integers, then we say that Γ is an integral graph. A graph Γ is determined by its spectrum if every graph cospectral to it is in fact isomorphic to it. In this paper, we investigate some algebraic properties of the Cayley graph Γ=Cayℤn,S, where n=pm (p is a prime integer and m∈ℕ) and S=a∈ℤn|a,n=1. First, we show that Γ is an integral graph. Also, we determine the automorphism group of Γ. Moreover, we show that Γ and Kv▽Γ are determined by their spectrum.http://dx.doi.org/10.1155/2021/6632206 |
| spellingShingle | Jia-Bao Liu S. Morteza Mirafzal Ali Zafari Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum Journal of Mathematics |
| title | Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum |
| title_full | Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum |
| title_fullStr | Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum |
| title_full_unstemmed | Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum |
| title_short | Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum |
| title_sort | some algebraic properties of a class of integral graphs determined by their spectrum |
| url | http://dx.doi.org/10.1155/2021/6632206 |
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