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- Title
Q(L)-spectra of two join graphs and infinite families of Q(L)-integral graphs.
- Authors
SUN Feng-mei; WANG Li-gong
- Abstract
Let G be a simple graph. The matrix Q(G)D(G)+A(G) is the signiess Laplacian matrix of G, where D(G) and A(G) is the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. The Laplacian matrix of G is the matrix L(G)D(G)-A(G). A graph iscalled L-integral (resp. Q-integral) if its (signiess) Laplacian spectrum consists entirely of integers. Let G1 and G2 be two graphs, and S(G) be the subdivision graph of G. Then the Svertex join of G1 and G2, denoted by G1 V G2 is obtained from S(G1) and G2 by joining each vertices of G1 to each vertices of G2. The Sedge join of G1 with G2, denoted by G1 V LG2 is obtained from S(G1) and G2 by joining all vertices of S(G1) corresponding to the edges of G1 with all vertices of G2. In this paper we obtain the Q-spectra and L-spectra of these two joins of graphs when G1 and G2 are regular graphs. As an application, some infinite families of Q-integral graphs and L-integral graphs are obtained.
- Subjects
LAPLACIAN matrices; INFINITE matrices; INTEGERS; VERTEX operator algebras; LEBESGUE integral
- Publication
Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao, 2013, Vol 26, Issue 4, p423
- ISSN
1006-8341
- Publication type
Article