文献类型：期刊文献

英文题名：Proof of a conjecture on communicability distance sum index of graphs

作者：Huang, Xueyi[1,2];Das, Kinkar Chandra[1]

机构：[1]Sungkyunkwan Univ, Dept Math, Suwon 16419, South Korea;[2]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2022

卷号：645

起止页码：278

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20221511940692);WOS:【SCI-EXPANDED(收录号:WOS:000806350200016)】；

基金：Acknowledgements The authors are much grateful to the anonymous referee for his/her valuable com-ments on our paper, which have considerably improved the presentation of this paper. X. Huang is supported by the National Natural Science Foundation of China (Grant No. 11901540) . K. C. Das is supported by National Research Foundation funded by the Korean government (Grant No. 2021R1F1A1050646) .

语种：英文

外文关键词：Communicability distance; Communicability distance sum index; Spectral decomposition; Graph eigenvalues; Lagrange multiplier theorem

摘要：Let G be a connected graph with adjacency matrix A, and let A = exp(A). The communicability distance between two vertices u and v of G is defined as xi uv = (Auu + Avv - 2Auv)1/2, and the communicability distance sum index (CDS index for short) of G is the sum of all communicability distances between vertices of G. In this paper, it is shown that the complete graph Kn is the unique graph attaining the minimum CDS index among all connected graphs of order n. This confirms a conjecture of Estrada (2012) [2]. Furthermore, some upper and lower bounds for the CDS index of graphs are provided. (C) 2022 Elsevier Inc. All rights reserved.