GRAPHS WHOSE Aα-SPECTRAL RADIUS DOES NOT EXCEED 2

被引：8

作者：

Wang, Jian Feng ^{[1
]}

Wang, Jing ^{[2
]}

Liu, Xiaogang ^{[2
]}

Belardo, Francesco ^{[3
]}

机构：

[1] Shandong Univ Technol, Sch Math & Stat, Zibo 255049, Peoples R China

[2] Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Peoples R China

[3] Univ Naples Federico II, Dept Math & Applicat R Caccioppoli, I-80126 Naples, Italy

来源：

DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2020年 / 40卷 / 02期

基金：

中国国家自然科学基金;

关键词：

A(alpha)-matrix; Smith graphs; limit point; spectral radius; index; SPECTRAL-RADIUS;

D O I：

10.7151/dmgt.2288

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A(G) and D(G) be the adjacency matrix and the degree matrix of a graph G, respectively. For any real alpha is an element of [0; 1], we consider A(alpha)(G) = D-alpha(G) + (1 - alpha)A(G) as a graph matrix, whose largest eigenvalue is called the A(alpha)-spectral radius of G. We first show that the smallest limit point for the A(alpha)-spectral radius of graphs is 2, and then we characterize the connected graphs whose A(alpha)-spectral radius is at most 2. Finally, we show that all such graphs, with four exceptions, are determined by their A(alpha)-spectra.

引用

页码：677 / 690

页数：14

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