On the minimum spectral radius of connected graphs of given order and size

被引：0

作者：

Cioaba, Sebastian M. ^{[1
]}

Gupta, Vishal ^{[1
]}

Marques, Celso ^{[2
]}

机构：

[1] Univ Delaware, Dept Math Sci, Delaware, OH 43015 USA

[2] Ctr Fed Educ Tecnol Celso Suckow Fonseca CEFET, Rio De Janeiro, Brazil

来源：

SPECIAL MATRICES | 2024年 / 12卷 / 01期

关键词：

spectral radius of a graph; adjacency matrix;

D O I：

10.1515/spma-2024-0027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we study a question of Hong from 1993 related to the minimum spectral radii of the adjacency matrices of connected graphs of given order and size. Hong asked if it is true that among all connected graphs of given number of vertices n n and number of edges e e , the graphs having minimum spectral radius (the minimizer graphs) must be almost regular, meaning that the difference between their maximum degree and their minimum degree is at most one. In this article, we answer Hong's question positively for various values of n n and e e , and in several cases, we determined the graphs with minimum spectral radius.

引用

页数：23