Cayley Picture Fuzzy Graphs and Interconnected Networks  

作　　者：Waheed Ahmad Khan Khurram Faiz Abdelghani Taouti 

机构地区：[1]Department of Mathematics,University of Education Lahore,Attock campus,Pakistan [2]ETS-Maths and NS Engineering Division,HCT,University City,Sharjah,United Arab Emirates

出　　处：《Intelligent Automation & Soft Computing》2023年第3期3317-3330,共14页智能自动化与软计算（英文）

摘　　要：Theory of the Cayley graphs is directly linked with the group theory.However,if there are uncertainties on the vertices or edges or both then fuzzy graphs have an extraordinary importance.In this perspective,numbers of generalηizations of fuzzy graphs have been explored in the literature.Among the others,picture fuzzy graph(PFG)has its own importance.A picture fuzzy graph(PFG)is a pair G=(C,D)defined on a H^(*)=(A,B),where C=(ηC,θ_(C),■_(C))is a picture fuzzy set on A and D=(ηD,θ_(D),■_(D))is a picture fuzzy set over the set B∈A×A such that for any edge mn∈ B with ηD(m,n)≤min(ηC(m),ηC(n)),θD(m,n)≤min(θC(m),θC(n))and ■_(D)(m,n)≥max(■_(C)(m),■_(C)(n)).In this manuscript,we introduce the notion of the Cayley picture fuzzy graphs on groups which is the generalization of the picture fuzzy graphs.Firstly,we discuss few important characteristics of the Cayley picture fuzzy graphs.We show that Cayley picture fuzzy graphs are vertex transitive and hence regular.Then,we investigate different types of Cayley graphs induced by the Cayley picture fuzzy graphs by using different types of cuts.We extensively discuss the term connectivity of the Cayley picture fuzzy graphs.Vertex connectivity and edge connectivity of the Cayley picture fuzzy graphs are also addressed.We also investigate the linkage between these two.Throughout,we provide the extensions of some characηteristics of both the PFGs and Cayley fuzzy graphs in the setting of Cayley picture fuzzy graphs.Finally,we provide the model of interconnected networks based on the Cayley picture fuzzy graphs.

关 键 词：Cayley picture fuzzy graphs strong CPFGs connected CPFGs cut sets of CPFGs 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]