Q(L)-spectra of two join graphs and infinite families of Q(L)-integral graphs

Feng Mei Sun, Li Gong Wang

科研成果: 期刊稿件文章同行评审

摘要

Let G be a simple graph. The matrix Q(G) = D(G) + A(G) is the signless 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 (signless) Laplacian spectrum consists entirely of integers. Let G 1 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 VG2 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 G 1 and G2 are regular graphs. As an application, some infinite families of Q-integral graphs and L-integral graphs are obtained.

源语言英语
页(从-至)423-428+435
期刊Fangzhi Gaoxiao Jichukexue Xuebao
26
4
出版状态已出版 - 12月 2013

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