The change of distance energy of some special complete multipartite graphs due to edge deletion

被引：12

作者：

Tian, Gui-Xian ^{[1
]}

Li, Yuan ^{[1
]}

Cui, Shu-Yu ^{[1
,2
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[2] Zhejiang Normal Univ, Xingzhi Coll, Jinhua 321004, Zhejiang, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2020年 / 584卷

基金：

中国国家自然科学基金;

关键词：

Complete multipartite graph; Distance energy; Distance energy change; Edge deletion; Quotient matrix; SPECTRA;

D O I：

10.1016/j.laa.2019.09.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let K-p1,K-p2,K-...pr be a complete r-partite graph with r >= 2 and p(i) >= 2. Varghese et al. (2018) [14] conjectured that the distance energy of K-p1,K-p2,K-...,K-pr is always increased when an edge is deleted. In this paper, we prove that it is true for K-p,K-p,K-...,K-p and the tripartite Turan graph T(n, 3). Subsequently, it is proved that, for any positive integer r, there exists a class of graphs that have r positive eigenvalues, but the distance energy of these graphs is always increased when an edge is deleted. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：438 / 457

页数：20

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