监测图边测地数的诺德豪斯-加德姆型结果

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-04-24 DOI:10.1016/j.dam.2025.04.040

Yingying Zhang , Fanfan Wang , Chenxu Yang

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引用次数: 0

摘要

Foucaud等人受距离边缘监测集（distance-edge-monitoring set）和边缘大地测量集（edge-geodetic set）两个概念的启发，提出了监测边缘大地测量集（edge-geodetic set）的概念，用于监测网络的链路，以检测和预防故障。图的顶点集称为监测边测地集（MEG-set），如果任何边的移除会改变集合中某些顶点对之间的距离。最小监测边测地集的基数称为监测边测地数。本文给出了一般图、树和单环图关于监测边测地数的nordhaus - gaddum型结果。此外，我们还刻画了到达边界的极值图。

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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Nordhaus–Gaddum-type results for monitoring edge-geodetic number of graphs

Inspired by two notions (distance-edge-monitoring set and edge-geodetic set), Foucaud et al. introduced the concept of monitoring edge-geodetic set, which is used to monitor the links of a network in order to detect and prevent failures. A vertex set of a graph is called a monitoring edge-geodetic set (MEG-set for short) if the removal of any edge changes the distance between some pair of vertices in the set. The cardinality of the minimum monitoring edge-geodetic set is called the monitoring edge-geodetic number. In this paper, we give Nordhaus–Gaddum-type results of general graphs, trees and unicyclic graphs with respect to monitoring edge-geodetic number. Moreover, we characterize the extremal graphs, which reach the bounds.

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.