文献类型：期刊文献

英文题名：Eigenvalues of the k-th power of a graph

作者：Das, Kinkar Ch[1];Guo, Ji-Ming[2]

机构：[1]Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea;[2]East China Univ Sci & Technol, Dept Math, Shanghai, Peoples R China

年份：2016

卷号：289

期号：13

起止页码：1585

外文期刊名：MATHEMATISCHE NACHRICHTEN

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000384865300002)】；

基金：The authors are much grateful to two anonymous referees for their valuable comments and corrections on our paper, which have considerably improved the presentation of this paper. The first author is supported by the National Research Foundation funded by the Korean government with Grant no. 2013R1A1A2009341. The second author is supported by the National Natural Science Foundation of China (No. 11371372).

语种：英文

外文关键词：Graph; adjacency matrix; spectral radius; k-th power of graph; Nordhaus-Gaddum-type inequality; diameter

摘要：The k-th power of a graph G, denoted by G(k), is a graph with the same set of vertices as G such that two vertices are adjacent in G(k) if and only if their distance in G is at most k. In this paper, we give the bounds on the spectral radius of T-k and G(k) (k >= 1). The Nordhausn-Gaddum-type inequality for the spectral radius of the graph G(k) is also presented. Moreover, we obtain an upper bound on the energy of the second power of graphs. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim