Infinitely many pairs of cospectral integral regular graphs  

作　　者：WANG Li-gong SUN Hao 

机构地区：[1]Department of Applied Mathematics, Northwestern Polytechnical University, Xi＇an 710072, China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2011年第3期280-286,共7页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China (10871158, 70871098);the Natural Science Basic Research Plan in Shaanxi Province of China (SJ08A01, 2007A09) and SRF for ROCS, SEM

摘　　要：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 Gs（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.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 Gs（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.

关 键 词：EIGENVALUE integral graph cospectral graph graph spectrum. 

分 类 号：O157.5[理学—数学] TP391.41[理学—基础数学]