Infinitely many pairs of cospectral integral regular graphs |
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Authors: | Li-gong Wang Hao Sun |
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Institution: | Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China. |
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Abstract: | A graph G is called integral if all the eigenvalues of the adjacency matrix A(G) of G are integers. In this paper, the graphs G
4(a, b) and G
5(a, b) with 2a+6b vertices are defined. We give their characteristic polynomials from matrix theory and prove that the (n+2)-regular graphs G
4(n, n+2) and G
5(n, n+2) are a pair of non-isomorphic connected cospectral integral regular graphs for any positive integer n. |
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Keywords: | Eigenvalue integral graph cospectral graph graph spectrum |
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