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运筹学学报 >

2020 , Vol. 24 >Issue 4: 128 - 134

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2020.04.011

单圈图的次大(拉普拉斯)分离度

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  • 1. 安庆师范大学数理学院, 安徽安庆 246133;
    2. 合肥幼儿师范高等专科学校公共教学部, 合肥 230013

收稿日期: 2018-03-21

  网络出版日期: 2020-11-18

基金资助

国家自然科学基金（No.11871077），安徽省自然科学基金（No.1808085MA04），安徽省高校自然科学基金（No.KJ2017A362）

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The second maximum (Laplacian) separator of unicyclic graphs

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  • 1. School of Mathematics and Physics, Anqing Normal University, Anqing 246133, Anhui, China;
    2. Department of Public Education, Hefei Preschool Education College, Hefei 230013, China

Received date: 2018-03-21

  Online published: 2020-11-18

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摘要

设G是一个n阶单圈图，λ1（G）、λ2（G）分别为图G的邻接矩阵的最大特征值与次大特征值，μ1（G）、μ2（G）分别为图G的拉普拉斯矩阵的最大特征值与次大特征值。图G的分离度定义为SA（G）=λ1（G）-λ2（G），拉普拉斯分离度定义为SL（G）=μ1（G）-μ2（G）。研究单圈图的（拉普拉斯）分离度，并分别给出了取得次大分离度和次大拉普拉斯分离度的极图。

关键词： 单圈图; 分离度; 拉普拉斯分离度

本文引用格式

余桂东, 阮征, 舒阿秀, 于涛 . 单圈图的次大(拉普拉斯)分离度[J]. 运筹学学报, 2020 , 24(4) : 128 -134 . DOI: 10.15960/j.cnki.issn.1007-6093.2020.04.011

Abstract

Let G be a unicyclic graph of order n, λ1(G) and λ2(G) be the largest eigenvalue and second largest eigenvalue of the adjacent matrix of G, μ1(G) and μ2(G) be the largest eigenvalue and second largest eigenvalue of the Laplacian matrix of G, respectively. The separator of G is defined as SA(G)=λ1(G) -λ2(G). The Laplacian separator of G is defined as SL(G)=μ1(G) -μ2(G). In this paper, we study the (Laplacian) separator of unicyclic graphs, and give the extremal graphs which attain the second maximum separator and second maximum Laplacian separator respectively.

Key words： unicyclic graph; separator; Laplacian separator

参考文献

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