{"title":"模糊中值图的结构特性","authors":"Anandhu Mohan, M. V. Dhanyamol, Sunil Mathew","doi":"10.1007/s12190-024-02197-y","DOIUrl":null,"url":null,"abstract":"<p>This paper investigates the relationship between fuzzy median graphs and blocks, which are important concepts in fuzzy graph theory, particularly in terms of connectivity. The main focus is on the fuzzy median property of a block that has at least four vertices and does not have any fuzzy bridges. The paper also examines the fuzzy median property of isomorphic images of median graphs and explores the median behavior of isometric subgraphs of a fuzzy median graph. Furthermore, the paper investigates the median property of fuzzy median graphs under graph operations. The main concern of the paper is to determine whether the union of two fuzzy median graphs retains fuzzy median behavior. The paper studies the connection between fully strong gated fuzzy graphs and fuzzy median graphs. It also explores whether the gate of an induced subgraph can also be in the median set of any triple of vertices. Additionally, the paper introduces a novel centrality measure called median centrality to identify the influential nodes in a network. The sum of the median centrality of all vertices in a fuzzy median graph will always be one.</p>","PeriodicalId":15034,"journal":{"name":"Journal of Applied Mathematics and Computing","volume":"58 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The structural properties of fuzzy median graphs\",\"authors\":\"Anandhu Mohan, M. V. Dhanyamol, Sunil Mathew\",\"doi\":\"10.1007/s12190-024-02197-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper investigates the relationship between fuzzy median graphs and blocks, which are important concepts in fuzzy graph theory, particularly in terms of connectivity. The main focus is on the fuzzy median property of a block that has at least four vertices and does not have any fuzzy bridges. The paper also examines the fuzzy median property of isomorphic images of median graphs and explores the median behavior of isometric subgraphs of a fuzzy median graph. Furthermore, the paper investigates the median property of fuzzy median graphs under graph operations. The main concern of the paper is to determine whether the union of two fuzzy median graphs retains fuzzy median behavior. The paper studies the connection between fully strong gated fuzzy graphs and fuzzy median graphs. It also explores whether the gate of an induced subgraph can also be in the median set of any triple of vertices. Additionally, the paper introduces a novel centrality measure called median centrality to identify the influential nodes in a network. The sum of the median centrality of all vertices in a fuzzy median graph will always be one.</p>\",\"PeriodicalId\":15034,\"journal\":{\"name\":\"Journal of Applied Mathematics and Computing\",\"volume\":\"58 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-08-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mathematics and Computing\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s12190-024-02197-y\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12190-024-02197-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
This paper investigates the relationship between fuzzy median graphs and blocks, which are important concepts in fuzzy graph theory, particularly in terms of connectivity. The main focus is on the fuzzy median property of a block that has at least four vertices and does not have any fuzzy bridges. The paper also examines the fuzzy median property of isomorphic images of median graphs and explores the median behavior of isometric subgraphs of a fuzzy median graph. Furthermore, the paper investigates the median property of fuzzy median graphs under graph operations. The main concern of the paper is to determine whether the union of two fuzzy median graphs retains fuzzy median behavior. The paper studies the connection between fully strong gated fuzzy graphs and fuzzy median graphs. It also explores whether the gate of an induced subgraph can also be in the median set of any triple of vertices. Additionally, the paper introduces a novel centrality measure called median centrality to identify the influential nodes in a network. The sum of the median centrality of all vertices in a fuzzy median graph will always be one.
期刊介绍：
JAMC is a broad based journal covering all branches of computational or applied mathematics with special encouragement to researchers in theoretical computer science and mathematical computing. Major areas, such as numerical analysis, discrete optimization, linear and nonlinear programming, theory of computation, control theory, theory of algorithms, computational logic, applied combinatorics, coding theory, cryptograhics, fuzzy theory with applications, differential equations with applications are all included. A large variety of scientific problems also necessarily involve Algebra, Analysis, Geometry, Probability and Statistics and so on. The journal welcomes research papers in all branches of mathematics which have some bearing on the application to scientific problems, including papers in the areas of Actuarial Science, Mathematical Biology, Mathematical Economics and Finance.
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