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运筹学学报 ›› 2014, Vol. 18 ›› Issue (3): 13-32.

• 运筹学 • 上一篇    下一篇

恰有两个Q-主特征值的三圈图

陈琳1, 黄琼湘2,*   

  1. 1. 新疆医科大学医学工程技术学院, 乌鲁木齐 830011,
    2. 新疆大学数学与系统科学学院, 乌鲁木齐 830046
  • 出版日期:2014-09-15 发布日期:2014-09-15
  • 通讯作者: 黄琼湘 E-mail:huangqx@xju.edu.cn
  • 基金资助:

    国家自然科学基金(Nos. 11261059, 11301452), 新疆医科大学科研创新基金(No. XJC-201237)

Tricyclic graphs  with exactly two Q-main eigenvalues

CHEN Lin1, HUANG Qiongxiang2,*   

  1. 1. College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China, 2. College of Mathematics and System Science, Xinjiang University, Urumqi 830046,  China
  • Online:2014-09-15 Published:2014-09-15

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摘要： 图G的无符号拉普拉斯 矩阵定义为图G的邻接矩阵与度对角矩阵的和, 其特征值称为图G的Q-特征值. 图G的一个Q-特征值称为Q-主特征值, 如果它有一个特征向量其分量的和不等于零. 确定了所有恰有两个Q-主特征值的三圈图.

关键词: 无符号拉普拉斯矩阵, Q-主特征值, 三圈图

Abstract: The signless Laplacian matrix of a graph G is defined to be the sum of its adjacency matrix and degree diagonal matrix, and its eigenvalues are called Q-eigenvalues of G.  A Q-eigenvalue of a graph G is called a  Q-main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this work, all tricyclic graphs with exactly two Q-main eigenvalues are determined.

Key words: signless Laplacian matrix, Q-main eigenvalue, tricyclic graph

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