On graphs with girth g and positive inertia index of [g]/2 1 and [g]/2

被引：1

作者：

Duan, Fang ^{[1
]}

Yang, Qi ^{[1
]}

机构：

[1] Xinjiang Normal Univ, Sch Math Sci, Urumqi 830054, Xinjiang, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2024年 / 683卷

基金：

中国国家自然科学基金;

关键词：

Positive inertia index; Girth; Extremal graph; SIGNED GRAPHS; NULLITY; NUMBER;

D O I：

10.1016/j.laa.2023.12.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a graph. The numbers of positive, negative and zero eigenvalues (including multiplicities) of the adjacency matrix A(G) are denoted by p(G), n(G) and eta(G), respectively. Traditionally, p(G) (resp. n(G)) is called the positive (resp. negative) inertia index of G. Suppose that a connected graph G has at least one cycle and let g be the length of the shortest cycle in G. In this paper, we prove p(G) >= [g/2 ] -1. Moreover, the extremal graphs corresponding to p(G) = [g/2 ] - 1 and p(G) = [g/2 ] are completely characterized, respectively. (c) 2023 Elsevier Inc. All rights reserved.

引用

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页码：98 / 110

页数：13

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