{"title":"Resistance distance in generalized core–satellite graphs","authors":"Qi Ni, Xiang-Feng Pan, Huan Zhou","doi":"10.1016/j.dam.2024.11.011","DOIUrl":null,"url":null,"abstract":"<div><div>The resistance distance between two vertices in a connected graph is defined as the effective resistance between the two nodes in the corresponding electric network after replacing each edge with a unit resistor. A generalized core–satellite graph is a graph formed by several satellite cliques not limited to having the same number of vertices all connected to a common satellite clique. In this paper, applying equivalent transformations in electric circuits and the principles of substitution and elimination, we derive an explicit expression for the resistance distance between arbitrary two vertices in a generalized core–satellite graph.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"362 ","pages":"Pages 100-108"},"PeriodicalIF":1.0000,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X24004815","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The resistance distance between two vertices in a connected graph is defined as the effective resistance between the two nodes in the corresponding electric network after replacing each edge with a unit resistor. A generalized core–satellite graph is a graph formed by several satellite cliques not limited to having the same number of vertices all connected to a common satellite clique. In this paper, applying equivalent transformations in electric circuits and the principles of substitution and elimination, we derive an explicit expression for the resistance distance between arbitrary two vertices in a generalized core–satellite graph.
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.
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