Q-integral complete r-partite graphs

Guopeng Zhao, Ligong Wang, Ke Li

科研成果: 期刊稿件文章同行评审

13 引用 (Scopus)

摘要

For a graph G of order n, the signless Laplacian matrix of G is Q(G)=D(G)+A(G), where A(G) is its adjacency matrix and D(G) is the diagonal matrix of the vertex degrees in G. The signless Laplacian characteristic polynomial (or Q-polynomial) of G is QG(x)=|x In-Q(G)|, where In is the n×n identity matrix. A graph G is called Q-integral if all the eigenvalues of its signless Laplacian characteristic polynomial QG(x) are integers. In this paper, we give a sufficient and necessary condition for complete r-partite graphs to be Q-integral, from which we construct infinitely many new classes of Q-integral graphs. Finally, we propose two basic open problems for further study.

源语言英语
页(从-至)1067-1077
页数11
期刊Linear Algebra and Its Applications
438
3
DOI
出版状态已出版 - 1 2月 2013

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