文献类型：期刊文献

英文题名：Sharp upper bounds of the spectral radius of a graph

作者：Guo, Ji-Ming[1];Wang, Zhi-Wen[1];Li, Xin[1]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai, Peoples R China

年份：2019

卷号：342

期号：9

起止页码：2559

外文期刊名：DISCRETE MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000478711900007)】；

基金：This research is supported by NSFC, PR China (No. 11371372)

语种：英文

外文关键词：Spectral radius; Upper bound; Graph

摘要：Let G be a simple connected graph with n vertices and m edges. The spectral radius rho(G) of G is the largest eigenvalue of its adjacency matrix. In this paper, we firstly consider the effect on the spectral radius of a graph by removing a vertex, and then as an application of the result, we obtain a new sharp upper bound of rho(G) which improves some known bounds: If (k-2)(k-3)/2 <= m - n <= k(k-3)/2, where k (3 <= k <= n) is an integer, then rho(G) <= root 2m - n - k + 5/2 + root 2m - 2n + 9/4. The equality holds if and only if G is a complete graph K-n, or K-4 - e, where K-4 - e is the graph obtained from K-4 by deleting some edge e. (C) 2019 Elsevier B.V. All rights reserved.