Infinitely many pairs of cospectral integral regular graphs

Li gong Wang; Hao Sun

doi:10.1007/s11766-011-2180-1

Infinitely many pairs of cospectral integral regular graphs

Li gong Wang, Hao Sun

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 G₄(a, b) and G₅(a, b) with 2a+6b vertices are defined. We give their characteristic polynomials from matrix theory and prove that the (n+2)-regular graphs G₄(n, n+2) and G₅(n, n+2) are a pair of non-isomorphic connected cospectral integral regular graphs for any positive integer n.

Original language	English
Pages (from-to)	280-286
Number of pages	7
Journal	Applied Mathematics
Volume	26
Issue number	3
DOIs	https://doi.org/10.1007/s11766-011-2180-1
State	Published - Sep 2011

Keywords

cospectral graph
Eigenvalue
graph spectrum
integral graph

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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 G4(a, b) and G5(a, b) with 2a+6b vertices are defined. We give their characteristic polynomials from matrix theory and prove that the (n+2)-regular graphs G4(n, n+2) and G5(n, n+2) are a pair of non-isomorphic connected cospectral integral regular graphs for any positive integer n.",

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AB - 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 G4(a, b) and G5(a, b) with 2a+6b vertices are defined. We give their characteristic polynomials from matrix theory and prove that the (n+2)-regular graphs G4(n, n+2) and G5(n, n+2) are a pair of non-isomorphic connected cospectral integral regular graphs for any positive integer n.

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KW - Eigenvalue

KW - graph spectrum

KW - integral graph

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Infinitely many pairs of cospectral integral regular graphs

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Keywords

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