文献类型：期刊文献

英文题名：Remoteness and distance eigenvalues of a graph

作者：Lin, Huiqiu[1];Das, Kinkar Ch.[2];Wu, Baoyindureng[3]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai, Peoples R China;[2]Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea;[3]Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China

年份：2016

卷号：215

起止页码：218

外文期刊名：DISCRETE APPLIED MATHEMATICS

收录：;EI(收录号：20164202912265);WOS:【SCI-EXPANDED(收录号:WOS:000385335000023)】；

基金：We thank the referees for their valuable comments which helped to improve the presentation of the paper. The first author is supported by the National Natural Science Foundation of China (Nos. 11401211 and 11471211), the China Postdoctoral Science Foundation (Nos. 2014M560303 and 2015T80404) and Fundamental Research Funds for the Central Universities (No. 222201414021). The second author is supported by the National Research Foundation funded by the Korean government with Grant No. 2013R1A1A2009341. The third author is supported by the National Natural Science Foundation of China by (No. 11571294) and by Xinjiang Talent Youth Project (No. 2013721012).

语种：英文

外文关键词：Remoteness; Distance matrix; Distance eigenvalues

摘要：Let G be a connected graph of order n with diameter d. Remoteness rho of G is the maximum average distance from a vertex to all others and partial derivative(1) >= ... >= partial derivative(n) are the distance eigenvalues of G. Aouchiche and Hansen (0000), Aouchiche and Hansen conjectured that rho + partial derivative(3) > 0 when d >= 3 and rho + partial derivative(left perpendicular7d//right perpendicular) > 0. In this paper, we confirm these two conjectures. Furthermore, we give lower bounds on partial derivative(n) + rho and partial derivative(1) - rho when G not congruent to K-n and the extremal graphs are characterized. (C) 2016 Elsevier B.V. All rights reserved.