文献类型：期刊文献

英文题名：The spectral radius of graphs with given independence number

作者：Lou, Zhenzhen[1,2];Guo, Ji-Ming[1]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China

年份：2022

卷号：345

期号：4

外文期刊名：DISCRETE MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000784327100027)】；

基金：This work is supported by National Natural Science Foundation of China (Nos. 12171154 and 12061074) , the China Postdoctoral Science Foundation (No. 2019M661398) .

语种：英文

外文关键词：Spectral radius; Independence number; Extremal graph; Bipartite graph; Tree

摘要：As a classic problem of spectral graph theory, Brualdi-Solheid problem asks which graph achieves the extremal (maximum or minimum) spectral radius for a given class of graphs. In this paper, we focus on this problem for graphs with fixed independence number. We first obtain the maximum spectral radius and unique extremal graph among all bipartite graphs of order n with independence number alpha. Secondly, we study the minimum spectral radius of graphs with fixed independence number. Let G(n,alpha) be the set of connected graphs of order n with independence number alpha. We show that tree has the minimum spectral radius over all graphs in G(n,alpha) provided that alpha >= [n/2], and determine all the extremal graphs in G(n,n-4). (c) 2021 Elsevier B.V. All rights reserved.