The structural properties of fuzzy median graphs

IF 2.4 3区数学 Q1 MATHEMATICS

Journal of Applied Mathematics and Computing Pub Date : 2024-08-06 DOI:10.1007/s12190-024-02197-y

Anandhu Mohan, M. V. Dhanyamol, Sunil Mathew

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Abstract

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.

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模糊中值图的结构特性

模糊中值图与块是模糊图论中的重要概念，尤其是在连接性方面，本文研究了模糊中值图与块之间的关系。主要重点是研究至少有四个顶点且没有任何模糊桥的块的模糊中值属性。论文还研究了中值图同构图像的模糊中值属性，并探讨了模糊中值图等距子图的中值行为。此外，本文还研究了模糊中值图在图操作下的中值属性。论文的主要关注点是确定两个模糊中值图的结合是否保留了模糊中值行为。论文研究了完全强门控模糊图与模糊中值图之间的联系。论文还探讨了诱导子图的门是否也能位于任意三顶点的中值集中。此外，论文还引入了一种名为中值中心度的新型中心度量，用于识别网络中具有影响力的节点。模糊中值图中所有顶点的中值中心度之和始终为 1。

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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来源期刊

Journal of Applied Mathematics and Computing Mathematics-Computational Mathematics

CiteScore

4.20

自引率

4.50%

发文量

131

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.