Disproof of a conjecture on the minimum spectral radius and the domination number

被引：1

作者：

Hu, Yarong ^{[1
,3
]}

Lou, Zhenzhen ^{[2
]}

Huang, Qiongxiang ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

[2] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

[3] Yuncheng Univ, Sch Math & Informat Technol, Yuncheng 044000, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2023年 / 677卷

基金：

中国国家自然科学基金;

关键词：

Spectral radius; Domination number; Minimizer graph; GRAPHS; TREES;

D O I：

10.1016/j.laa.2023.08.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Gn,& gamma; be the set of all connected graphs on n vertices with domination number & gamma;. A graph is called a minimizer graph if it attains the minimum spectral radius among Gn,& gamma;. Very recently, Liu, Li and Xie (2023) [17] proved that the minimizer graph over all graphs in Gn,& gamma; must be a tree. Moreover, they determined the minimizer graph among Gn,Ln21 for even n, and posed the conjecture on the minimizer graph among Gn,L n2 1 for odd n. In this paper, we disprove the conjecture and completely determine the unique minimizer graph among Gn,L n2 1 for odd n. & COPY; 2023 Published by Elsevier Inc.

引用

页码：237 / 253

页数：17