Distribution of Laplacian eigenvalues of graphs

被引：8

作者：

Das, Kinkar Ch. ^{[1
]}

Mojallal, Seyed Ahmad ^{[1
]}

Trevisan, Vilmar ^{[2
]}

机构：

[1] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

[2] Univ Fed Rio Grande do Sul, Inst Matemat, BR-91509900 Porto Alegre, RS, Brazil

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2016年 / 508卷

基金：

新加坡国家研究基金会;

关键词：

Graph; Laplacian matrix; Laplacian eigenvalues; Clique number; ENERGY; SPECTRUM;

D O I：

10.1016/j.laa.2016.06.039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a graph of order n with m edges and clique number omega. Let mu(1) >= mu(2) >= ... >= mu(n) = 0 be the Laplacian eigenvalues of G and let sigma = sigma(G) (1 <= sigma <= n) be the largest positive integer such that mu(sigma) >= 2m/n. In this paper we study the relation between a and w. In particular, we provide the answer to Problem 2.3 raised in Pirzada and Ganie (2015) [15]. Moreover, we characterize all connected threshold graphs with sigma < w - 1, sigma = omega - 1 and sigma > w - 1. We obtain Nordhaus-Gaddum-type results for sigma. Some relations between a with other graph invariants are obtained. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：48 / 61

页数：14

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