First eigenvalue of nonsingular mixed graphs with given number of pendant vertices

被引：2

作者：

Liu, Ruifang ^{[1
]}

Jia, Huicai ^{[2
]}

Yuan, Jinjiang ^{[1
]}

机构：

[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China

[2] Henan Inst Engn, Coll Sci, Zhengzhou 451191, Henan, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 453卷

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Nonsingular mixed graph; Laplacian matrix; First eigenvalue; Pendant vertices; ALGEBRAIC CONNECTIVITY; SIGNLESS LAPLACIAN; LEAST EIGENVALUE; FIXED GIRTH;

D O I：

10.1016/j.laa.2014.04.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a mixed graph and L(G) be the Laplacian matrix of the mixed graph G. The first eigenvalue of G is referred to the least nonzero eigenvalue of L(G). Let MG(n, k) be the set of nonsingular mixed graphs with n vertices and k pendant vertices, where n >= 4. In this paper, up to a signature matrix, we determine the unique graph with the minimal first eigenvalue among all graphs hi MG(n, k). Thus we obtain a lower bound for the first eigenvalue of a mixed graph in terms of the number of pendant vertices. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：28 / 43

页数：16

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