文献类型：期刊文献

英文题名：Maximum degree and spectral radius of graphs in terms of size

作者：Wang, Zhiwen[1]; Guo, Ji-Ming[2]

机构：[1] School of Mathematical Sciences, NanKai University, Tianjin, 300071, China; [2] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2022

外文期刊名：arXiv

收录：EI(收录号：20220338437)

语种：英文

外文关键词：Graph theory - Laplace transforms - Machine learning

摘要：Research on the relationship of the (signless Laplacian) spectral radius of a graph with its structure properties is an important research project in spectral graph theory. Denote by ρ(G) and q(G) the spectral radius and the signless Laplacian spectral radius of a graph G, respectively. Let k ≥ 0 be a fixed integer and G be a graph of size m which is large enough. We show that if ρ(G) ≥ √m ? k, then C4 ? G or K1,m?k ? G. Furthermore, we prove that if q(G) ≥ m ? k, then K1,m?k ? G. Both these two results extend some known results. Copyright ? 2022, The Authors. All rights reserved.