{"title":"Neighbourhood and competition graphs under fuzzy incidence graph and its application","authors":"Sk Rabiul Islam, Madhumangal Pal","doi":"10.1007/s40314-024-02928-8","DOIUrl":null,"url":null,"abstract":"<p>Competition graphs, which are mathematical representations of competitive relationships among entities, have found applications in various domains. This article introduces and explores several types of graphs, including fuzzy incidence competition graphs, fuzzy incidence neighborhood graphs, p-competition fuzzy incidence graphs, m-step fuzzy incidence competition graphs, and m-step fuzzy incidence neighborhood graphs. We establish sufficient conditions under which an edge is independent strong or independent incidence strong. Relation between competition graphs of isomorphic fuzzy incidence digraphs is established. Through rigorous analysis, several intriguing results concerning these graphs are derived. Additionally, at the end of the article, we evaluate a group of researchers using fuzzy incidence graphs to identify the most influential member within the group.\n</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"197 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s40314-024-02928-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Competition graphs, which are mathematical representations of competitive relationships among entities, have found applications in various domains. This article introduces and explores several types of graphs, including fuzzy incidence competition graphs, fuzzy incidence neighborhood graphs, p-competition fuzzy incidence graphs, m-step fuzzy incidence competition graphs, and m-step fuzzy incidence neighborhood graphs. We establish sufficient conditions under which an edge is independent strong or independent incidence strong. Relation between competition graphs of isomorphic fuzzy incidence digraphs is established. Through rigorous analysis, several intriguing results concerning these graphs are derived. Additionally, at the end of the article, we evaluate a group of researchers using fuzzy incidence graphs to identify the most influential member within the group.
期刊介绍：
Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics).
The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.
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