On the Ger\v{s}gorin disks of distance matrices of graphs

IF 0.7 4区 数学 Q2 Mathematics
M. Aouchiche, B. Rather, Issmail El Hallaoui
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引用次数: 1

Abstract

For a simple connected graph $G$, let $D(G)$, $Tr(G)$, $D^{L}(G)=Tr(G)-D(G)$, and $D^{Q}(G)=Tr(G)+D(G)$ be the distance matrix, the diagonal matrix of the vertex transmissions, the distance Laplacian matrix, and the distance signless Laplacian matrix of $G$, respectively. Atik and Panigrahi [2] suggested the study of the problem: Whether all eigenvalues, except the spectral radius, of $ D(G) $ and $ D^{Q}(G) $ lie in the smallest Ger\v{s}gorin disk? In this paper, we provide a negative answer by constructing an infinite family of counterexamples.
图的距离矩阵的Ger\v{s}gorin盘
对于简单连通图$G$,设$D(G)$、$Tr(G)$、$D^{L}(G)=Tr(G)-D(G)$和$D^{Q}(G)=Tr(G)+D(G)$分别为$G$的距离矩阵、顶点传递的对角矩阵、距离拉普拉斯矩阵和距离无符号拉普拉斯矩阵。Atik和Panigrahi[2]提出了一个问题的研究:$ D(G) $和$ D^{Q}(G) $的所有特征值,除了谱半径,是否都在最小的Ger\v{s}gorin圆盘上?在本文中,我们通过构造一个无穷反例族来给出一个否定的答案。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
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