运筹学学报 ›› 2019, Vol. 23 ›› Issue (1): 81-89.doi: 10.15960/j.cnki.issn.1007-6093.2019.01.009

• 运筹学 • 上一篇    下一篇

三圈图的无符号拉普拉斯谱半径

陈媛媛1, 王国平2,*   

  1. 1. 新疆大学数学与系统科学学院, 乌鲁木齐 830046;
    2. 新疆师范大学数学科学学院, 乌鲁木齐 830046
  • 收稿日期:2016-12-26 出版日期:2019-03-15 发布日期:2019-03-15
  • 通讯作者: 王国平 E-mail:xj.wgp@163.com
  • 基金资助:

    国家自然科学基金(No.11461071)

On the signless Laplacian spectral radius of tricyclic graphs

CHEN Yuanyuan1, WANG Guoping2,*   

  1. 1. College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China;
    2. School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830046, China
  • Received:2016-12-26 Online:2019-03-15 Published:2019-03-15

摘要:

假设图G的点集是VG)={v1v2,…,vn},用dviG)表示图G中点vi的度,令AG)表示G的邻接矩阵,DG)是对角线上元素等于dviG)的n×n对角矩阵,QG)=DG)+AG)是G的无符号拉普拉斯矩阵,QG)的最大特征值是G的无符号拉普拉斯谱半径.现确定了所有点数为n的三圈图中无符号拉普拉斯谱半径最大的图的结构.

关键词: 无符号拉普拉斯谱半径, 三圈图

Abstract:

Suppose that the vertex set of a graph G is V(G)={v1,v2,…,vn}. Then we denote by dvi(G) the degree of vi in G. Let A(G) be the adjacent matrix of G and D(G) be the n×n diagonal matrix with its (i,i)-entry equal to dvi(G). Then Q(G)=D(G)+A(G) is the signless Laplacian matrix of G. The signless Laplacian spectral radius of G is the largest eigenvalue of Q(G). In this paper we determine the extremal graph with maximum signless Laplacian spectral radius among all tricyclic graphs of order n.

Key words: signless Laplacian spectral radius, tricyclic graph

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