Fuzzy indices of some graphs with applications

IF 1.2 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Acta Informatica Pub Date : 2026-10-15 DOI:10.1007/s00236-026-00548-9

Bilal Ahmad Rather, Hilal Ahmad Ganie, Parvez Ali

{"title":"Fuzzy indices of some graphs with applications","authors":"Bilal Ahmad Rather, Hilal Ahmad Ganie, Parvez Ali","doi":"10.1007/s00236-026-00548-9","DOIUrl":null,"url":null,"abstract":"<div>We evaluate the closed forms of the fuzzy topological indices for fuzzy graph structures: the friendship graph and the windmill graph. General expressions are derived for the first and second fuzzy Zagreb indices, the fuzzy Randic index, the fuzzy harmonic index, the fuzzy F-index, the fuzzy Misbalance Prodeg index, the fuzzy Sombor index, and the fuzzy Nirmala index. The formulas are established for arbitrary vertex and edge membership values satisfying the Rosenfeld condition, and therefore apply to a broad class of admissible fuzzy graph structures. Suitable choices of membership values yield explicit closed forms for the fuzzy friendship graph \\(F_n\\) and the fuzzy windmill graph \\(W_{k,n}\\). The analysis also identifies inconsistencies in previously reported formulas, particularly those arising from incorrect fuzzy degrees, unspecified parameters, and edge memberships that do not agree with the stated graph structures [14]. The practical relevance of the proposed indices is demonstrated through an emergency medical referral network modeled by \\(F_3\\) and a renewable-energy microgrid represented by \\(W_{4,2}\\), where comparisons between normal and stressed operating conditions reveal changes in connectivity, balance, and system reliability.</div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"63 4","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Informatica","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1007/s00236-026-00548-9","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}

引用次数: 0

Abstract

We evaluate the closed forms of the fuzzy topological indices for fuzzy graph structures: the friendship graph and the windmill graph. General expressions are derived for the first and second fuzzy Zagreb indices, the fuzzy Randic index, the fuzzy harmonic index, the fuzzy F-index, the fuzzy Misbalance Prodeg index, the fuzzy Sombor index, and the fuzzy Nirmala index. The formulas are established for arbitrary vertex and edge membership values satisfying the Rosenfeld condition, and therefore apply to a broad class of admissible fuzzy graph structures. Suitable choices of membership values yield explicit closed forms for the fuzzy friendship graph \(F_n\) and the fuzzy windmill graph \(W_{k,n}\). The analysis also identifies inconsistencies in previously reported formulas, particularly those arising from incorrect fuzzy degrees, unspecified parameters, and edge memberships that do not agree with the stated graph structures [14]. The practical relevance of the proposed indices is demonstrated through an emergency medical referral network modeled by \(F_3\) and a renewable-energy microgrid represented by \(W_{4,2}\), where comparisons between normal and stressed operating conditions reveal changes in connectivity, balance, and system reliability.

查看原文本刊更多论文

若干图的模糊指标及其应用

我们评价了模糊图结构的模糊拓扑指标的封闭形式：友谊图和风车图。推导了第一、第二模糊Zagreb指数、模糊Randic指数、模糊harmonic指数、模糊f指数、模糊Misbalance Prodeg指数、模糊Sombor指数和模糊Nirmala指数的一般表达式。建立了满足Rosenfeld条件的任意顶点和边隶属度值的公式，从而适用于广泛的可容许模糊图结构。选取合适的隶属度值可得到模糊友谊图\(F_n\)和模糊风车图\(W_{k,n}\)的明确封闭形式。分析还确定了先前报告的公式中的不一致之处，特别是那些由不正确的模糊度、未指定的参数和与所述图结构[14]不一致的边隶属关系引起的不一致之处。通过以\(F_3\)为模型的紧急医疗转诊网络和以\(W_{4,2}\)为代表的可再生能源微电网，证明了所提出指标的实际相关性，其中正常和压力运行条件之间的比较揭示了连通性，平衡和系统可靠性的变化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Acta Informatica 工程技术-计算机：信息系统

CiteScore

2.40

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Acta Informatica provides international dissemination of articles on formal methods for the design and analysis of programs, computing systems and information structures, as well as related fields of Theoretical Computer Science such as Automata Theory, Logic in Computer Science, and Algorithmics. Topics of interest include: • semantics of programming languages • models and modeling languages for concurrent, distributed, reactive and mobile systems • models and modeling languages for timed, hybrid and probabilistic systems • specification, program analysis and verification • model checking and theorem proving • modal, temporal, first- and higher-order logics, and their variants • constraint logic, SAT/SMT-solving techniques • theoretical aspects of databases, semi-structured data and finite model theory • theoretical aspects of artificial intelligence, knowledge representation, description logic • automata theory, formal languages, term and graph rewriting • game-based models, synthesis • type theory, typed calculi • algebraic, coalgebraic and categorical methods • formal aspects of performance, dependability and reliability analysis • foundations of information and network security • parallel, distributed and randomized algorithms • design and analysis of algorithms • foundations of network and communication protocols.