文献类型：期刊文献

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

作者：Wang, Zhi-Wen[1];Guo, Ji-Ming[1]

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

年份：2020

卷号：601

起止页码：101

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20201808608861);WOS:【SCI-EXPANDED(收录号:WOS:000537681300005)】；

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

语种：英文

外文关键词：Spectral radius; Coalescence; Contract

摘要：For a graph G, the spectral radius rho(G) of G is the largest eigenvalue of its adjacency matrix. The coalescence of two graphs H with a root v and K with a root w is obtained by identifying v and w from disjoint union of H and K. In this paper, we investigate the upper bounds of the spectral radius of the coalescence of two graphs, which generalize some results by Passbani and Salemi in 2019. Furthermore, we show that if the graph G(u,v)* is obtained from a connected graph G by contracting the internal edge uv which not contained in any triangle of G, then rho(G) <= rho(G(u,v)*), the corresponding extremal graphs are characterized completely, and also extend a result of Hoffman and Smith. As an application, a new sharp upper bound on the spectral radius of a tree is provided. (C) 2020 Elsevier Inc. All rights reserved.