文献类型：期刊文献

英文题名：On the Dα-spectra of graphs

作者：Lin, Huiqiu[1];Xue, Jie[2];Shu, Jinlong[3]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai, Peoples R China;[2]Zhengzhou Univ, Sch Math & Stat, Zhengzhou, Henan, Peoples R China;[3]East China Normal Univ, Dept Comp Sci & Technol, Shanghai, Peoples R China

年份：2021

卷号：69

期号：6

起止页码：997

外文期刊名：LINEAR & MULTILINEAR ALGEBRA

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000469717900001)】；

基金：The first author was supported by the National Natural Science Foundation of China [grant number 11401211] and Fundamental Research Funds for the Central Universities [grant number 222201714049]. The third author was supported by the National Natural Science Foundation of China [grant number 11471121].

语种：英文

外文关键词：D-alpha-eigenvalue; extremal graph; cospectrality

摘要：Let G be a connected graph with distance matrix be the diagonal matrix of vertex transmissions of G. For any , the -matrix of G is defined as D-alpha(G) = alpha Tr(G) + (1 - alpha) D(G). In this paper, we study the -spectra of graphs. Firstly, the -eigenvalues of some special graphs are presented. Then we give a lower bound on the kth smallest -eigenvalue of graphs, and the extremal graphs are characterized. Also, several graph transformations on the -spectral radius are given, as applications, some extremal graphs with given structure parameters are characterized. Finally, we give some properties when two graphs have the same -spectra and several graphs are proved to be determined by their -spectra.