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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
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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| Summary: | 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. |
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| ISSN: | 2314-4629 2314-4785 |