Spectral extremal graphs for intersecting cliques

被引：24

作者：

Desai, Dheer Noal ^{[1
]}

Kang, Liying ^{[2
]}

Li, Yongtao ^{[3
]}

Ni, Zhenyu ^{[4
]}

Tait, Michael ^{[5
]}

Wang, Jing ^{[2
]}

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[3] Hunan Univ, Sch Math, Changsha, Peoples R China

[4] Hainan Univ, Dept Math, Haikou 570228, Hainan, Peoples R China

[5] Villanova Univ, Dept Math & Stat, Villanova, PA 19085 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2022年 / 644卷

基金：

美国国家科学基金会;

关键词：

Spectral radius; Intersecting cliques; Extremal graph; Stability method; RADIUS; EIGENVALUES; BOUNDS; PROOF;

D O I：

10.1016/j.laa.2022.03.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The (k, r)-fan is the graph consisting of k copies of the complete graph Kr which intersect in a single vertex, and is denoted by Fk,r. Erdos et al. (1995) [14] determined the maximum number of edges in an n-vertex graph that does not contain F(k,3 )as a subgraph. Furthermore, Chen et al. (2003) [5] proved the analogous result on F-k,F-r for the general case r >= 3. In this paper, we show that for sufficiently large n, the graphs of order n that contain no copy of F-k,F-r and attain the maximum spectral radius are also edge-extremal. That is, such graphs must have ex(n, F-k,F-r) edges. (C)& nbsp;2022 Elsevier Inc. All rights reserved.

引用

页码：234 / 258

页数：25

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