给定边数且直径为2的图的最小距离不平衡性

IF 1 Q1 MATHEMATICS

Discrete Mathematics Letters Pub Date : 2021-11-16 DOI:10.47443/dml.2021.s205

Kexiang Xu, Peiqi Yao

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引用次数: 2

摘要

对于一个图G，对于G的两个不同的顶点u和v，设nG(u, v)是G中G中离u比离v更近的顶点的个数。G的距离不平衡性是|nG(u, v)−nG(v, u)|对所有G的不同顶点u和v的无序对的和。我们确定了具有给定边数的2自中心图的最小距离不平衡性。我们还确定了具有至少一个通用顶点和给定边数的图的最小距离不平衡性。

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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Minimum Distance-Unbalancedness of Graphs With Diameter 2 and Given Number of Edges

For a graph G, and for two distinct vertices u and v of G, let nG(u, v) be the number of vertices of G that are closer in G to u than to v. The distance-unbalancedness of G is the sum of |nG(u, v)− nG(v, u)| over all unordered pairs of distinct vertices u and v of G. We determine the minimum distance-unbalancedness of 2-self-centered graphs with given number of edges. We also determine the minimum distance-unbalancedness of graphs with at least one universal vertex and given number of edges.

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来源期刊

Discrete Mathematics Letters Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

12 weeks