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运筹学学报 ›› 2012, Vol. 16 ›› Issue (2): 23-31.

• 运筹学 • 上一篇    下一篇

Q整图新类

 王力工1, 陈彦青1   

  1. 1. 西北工业大学理学院应用数学系，西安，710072
  • 出版日期:2012-06-15 发布日期:2012-06-15
  • 通讯作者: 王力工

Some new families of Q-integral graphs

 WANG  Li-Gong1, CHEN  Yan-Qing1   

  1. 1. Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an, 710072, China
  • Online:2012-06-15 Published:2012-06-15
  • Supported by:

    Supported by the National Natural Science Foundation of China (No.11171273), the Natural Science Foundation of Shaanxi Province (No.SJ08A01) and SRF for ROCS, SEM.

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被引次数

2

摘要： 对于一个简单图G, 方阵Q(G)=D(G)+A(G)称为G的无符号拉普拉斯矩阵,其中D(G)和A(G)分别为G的度对角矩阵和邻接矩阵. 一个图是Q整图是指该图的无符号拉普拉斯矩阵的特征值全部为整数.首先通过Stanic 得到的六个顶点数目较小的Q整图，构造出了六类具有无穷多个的非正则的Q整图. 进而,通过图的笛卡尔积运算得到了很多的Q整图类. 最后, 得到了一些正则的Q整图.

关键词: 无符号拉普拉斯谱, Q整图, 整图, 整特征值

Abstract:  Let G be a simple graph. The matrix Q(G)=D(G)+A(G) denotes the signless Laplacian matrix of G, where D(G) and A(G) denote the diagonal matrix and the adjacency matrix of G respectively. A graph is called Q-integral if its signless Laplacian spectrum consists entirely of integers. In this paper, we firstly construct six infinite classes of nonregular Q-integral graphs from the known six smaller Q-integral graphs identified by Stani\'{c}.  Furthermore, we obtain large families of Q-integral graphs by  the Cartesian product of graphs. Finally, we obtain some regular Q-integral graphs.

Key words:  signless Laplacian spectrum, Q-integral graph, integral graph, integral eigenvalues