图的最小状态、匹配与支配

IF 1.5 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Computer Journal Pub Date : 2020-03-01 DOI:10.1093/comjnl/bxaa057

Caixia Liang;Bo Zhou;Haiyan Guo

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引用次数: 7

摘要

给定一个图，一个顶点的状态是该顶点与所有其他顶点之间距离的总和。图的最小状态是该图的所有顶点的状态的最小值。我们给出了具有固定阶和匹配数（分别为支配数）的连通图的最小状态的一个尖锐上界，并刻画了实现该上界的唯一树。我们还确定了唯一树，使得当顺序和匹配数（分别为支配数）固定时，其最小状态尽可能小。

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 Status, Matching and Domination of Graphs

Given a graph, the status of a vertex is the sum of the distances between the vertex and all other vertices. The minimum status of a graph is the minimum of statuses of all vertices of this graph. We give a sharp upper bound for the minimum status of a connected graph with fixed order and matching number (domination number, respectively) and characterize the unique trees achieving the bound. We also determine the unique tree such that its minimum status is as small as possible when order and matching number (domination number, respectively) are fixed.

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来源期刊

Computer Journal 工程技术-计算机：软件工程

CiteScore

3.60

自引率

7.10%

发文量

164

审稿时长

4.8 months

期刊介绍： The Computer Journal is one of the longest-established journals serving all branches of the academic computer science community. It is currently published in four sections.