Note on the sum of the smallest and largest eigenvalues of a triangle-free graph

被引：5

作者：

Csikvari, Peter ^{[1
,2
]}

机构：

[1] Alfred Renyi Inst Math, Realtanoda Utca 13-15, H-1053 Budapest, Hungary

[2] Eotvos Lorand Univ, Pazmany Peter Setany 1-C, H-1117 Budapest, Hungary

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2022年 / 650卷

关键词：

Eigenvalues; Triangle-free graphs;

D O I：

10.1016/j.laa.2022.06.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a triangle-free graph on n vertices with adjacency matrix eigenvalues mu 1(G) >= mu(2)(G) >= . . . >= mu(n)(G). In this paper we study the quantity mu(1)(G) + mu(n)(G). We prove that for any triangle-free graph G we have mu(1)(G) + mu(n)(G) <= (3 - 2 root 2)n. This was proved for regular graphs by Brandt, we show that the condition on regularity is not necessary. We also prove that among triangle-free strongly regular graphs the Higman-Sims graph achieves the maximum of mu(1)(G) + mu n(G)/n . (C) 2022 Elsevier Inc. All rights reserved.

引用

页码：92 / 97

页数：6