三圈图的无符号拉普拉斯谱半径

doi:10.15960/j.cnki.issn.1007-6093.2019.01.009

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

三圈图的无符号拉普拉斯谱半径

陈媛媛¹, 王国平^2,*

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 Guoping^2,*

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/Abstract

摘要：

假设图G的点集是V（G）={v₁，v₂，…，v_n}，用d_{v_i}（G）表示图G中点v_i的度，令A（G）表示G的邻接矩阵，D（G）是对角线上元素等于d_{v_i}（G）的n×n对角矩阵，Q（G）=D（G）+A（G）是G的无符号拉普拉斯矩阵，Q（G）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,…,v_n}. Then we denote by d_{v_i}(G) the degree of v_i 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 d_{v_i}(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

中图分类号:

O157.5

陈媛媛, 王国平. 三圈图的无符号拉普拉斯谱半径[J]. 运筹学学报, 2019, 23(1): 81-89.

CHEN Yuanyuan, WANG Guoping. On the signless Laplacian spectral radius of tricyclic graphs[J]. Operations Research Transactions, 2019, 23(1): 81-89.

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三圈图的无符号拉普拉斯谱半径

On the signless Laplacian spectral radius of tricyclic graphs

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