THE VERTEX CONNECTIVITY AND THE THIRD LARGEST EIGENVALUE IN REGULAR (MULTI-)GRAPHS

被引：0

作者：

Ma, Tingyan ^{[1
,2
]}

Wang, Ligong ^{[1
,2
]}

Hu, Yang ^{[1
,2
]}

机构：

[1] Northwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China

[2] Northwestern Polytech Univ, Xian Budapest Joint Res Ctr Combinator, Xian 710129, Shaanxi, Peoples R China

来源：

ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2024年 / 40卷

关键词：

Eigenvalue; Vertex connectivity; Regular graph; Multigraph; DISJOINT SPANNING-TREES; ALGEBRAIC CONNECTIVITY; GRAPHS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a simple graph or a multigraph. The vertex connectivity kappa(G) of G is the minimum size of a vertex set S such that G -S is disconnected or has only one vertex. We denote by lambda(3)(G) the third largest eigenvalue of the adjacency matrix of G. In this paper, we present an upper bound for lambda(3)(G) in a d-regular (multi-)graph G which guarantees that kappa(G) >= t + 1, which is based on the result of Abiad et al. [Spectral bounds for the connectivity of regular graphs with given order. Electron. J. Linear Algebra 34:428-443, 2018]. Furthermore, we improve the upper bound for lambda 3(G) in a d-regular multigraph which assures that kappa(G) >= 2.

引用

页码：322 / 332

页数：11

共 24 条

[1] SPECTRAL BOUNDS FOR THE CONNECTIVITY OF REGULAR GRAPHS WITH GIVEN ORDER [J].