标题：GRAPHS WHOSE A(alpha)-SPECTRAL RADIUS DOES NOT EXCEED 2
作者：Wang, Jian Feng; Wang, Jing; Liu, Xiaogang; Belardo, Francesco
作者机构：[Wang, Jian Feng] Shandong Univ Technol, Sch Math & Stat, Zibo 255049, Peoples R China.; [Wang, Jing; Liu, Xiaogang] Northwestern Polytech Univ, Dep 更多
通讯作者地址：[Wang, JF]Shandong Univ Technol, Sch Math & Stat, Zibo 255049, Peoples R China.
来源：DISCUSSIONES MATHEMATICAE GRAPH THEORY
关键词：A(alpha)-matrix; Smith graphs; limit point; spectral radius; index
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.