Maximum degree and spectral radius of graphs in terms of size

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Algebraic Combinatorics Pub Date : 2024-01-20 DOI:10.1007/s10801-023-01289-5

Zhiwen Wang, Ji-Ming Guo

引用次数: 0

Abstract

Denote by \(\rho (G)\) and \(\kappa (G)\) the spectral radius and the signless Laplacian spectral radius of a graph G, respectively. Let \(k\ge 0\) be a fixed integer and G be a graph of size m which is large enough. We show that if \(\rho (G)\ge \sqrt{m-k}\), then \(C_4\subseteq G\) or \(K_{1,m-k}\subseteq G\). Moreover, we prove that if \(\kappa (G)\ge m-k+1\), then \(K_{1,m-k}\subseteq G\). Both these results extend some known results.

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图的最大度和谱半径大小

用 \(\rho (G)\) 和 \(\kappa (G)\) 分别表示图 G 的谱半径和无符号拉普拉斯谱半径。让 \(k\ge 0\) 是一个固定整数，G 是一个大小为 m 且足够大的图。我们证明，如果 \(\rho (G)\ge \sqrt{m-k}\), 那么 \(C_4\subseteq G\) 或者 \(K_{1,m-k}\subseteq G\).此外，我们还证明了如果\(\kappa (G)\ge m-k+1\)，那么\(K_{1,m-k}subseteq G\).这两个结果都扩展了一些已知结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebraic Combinatorics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics. The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.