Cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers.

A parameter is a numerical factor whose values help us to identify a system. Connectivity parameters are essential in the analysis of connectivity of various kinds of networks. In graphs, the strength of a cycle is always one. But, in a fuzzy incidence graph (FIG), the strengths of cycles may vary e...

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Autores principales:	Irfan Nazeer, Tabasam Rashid, Muhammad Tanveer Hussain
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/71727535ed8d4863b463acb557afc874
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spelling	oai:doaj.org-article:71727535ed8d4863b463acb557afc8742021-12-02T20:17:28ZCyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers.1932-620310.1371/journal.pone.0257642https://doaj.org/article/71727535ed8d4863b463acb557afc8742021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0257642https://doaj.org/toc/1932-6203A parameter is a numerical factor whose values help us to identify a system. Connectivity parameters are essential in the analysis of connectivity of various kinds of networks. In graphs, the strength of a cycle is always one. But, in a fuzzy incidence graph (FIG), the strengths of cycles may vary even for a given pair of vertices. Cyclic reachability is an attribute that decides the overall connectedness of any network. In graph the cycle connectivity (CC) from vertex a to vertex b and from vertex b to vertex a is always one. In fuzzy graph (FG) the CC from vertex a to vertex b and from vertex b to vertex a is always same. But if someone is interested in finding CC from vertex a to an edge ab, then graphs and FGs cannot answer this question. Therefore, in this research article, we proposed the idea of CC for FIG. Because in FIG, we can find CC from vertex a to vertex b and also from vertex a to an edge ab. Also, we proposed the idea of CC of fuzzy incidence cycles (FICs) and complete fuzzy incidence graphs (CFIGs). The fuzzy incidence cyclic cut-vertex, fuzzy incidence cyclic bridge, and fuzzy incidence cyclic cut pair are established. A condition for CFIG to have fuzzy incidence cyclic cut-vertex is examined. Cyclic connectivity index and average cyclic connectivity index of FIG are also investigated. Three different types of vertices, such as cyclic connectivity increasing vertex, cyclically neutral vertex and, cyclic connectivity decreasing vertex, are also defined. The real-life applications of CC of FIG in a highway system of different cities to minimize road accidents and a computer network to find the best computers among all other computers are also provided.Irfan NazeerTabasam RashidMuhammad Tanveer HussainPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 9, p e0257642 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Irfan Nazeer Tabasam Rashid Muhammad Tanveer Hussain Cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers.
description	A parameter is a numerical factor whose values help us to identify a system. Connectivity parameters are essential in the analysis of connectivity of various kinds of networks. In graphs, the strength of a cycle is always one. But, in a fuzzy incidence graph (FIG), the strengths of cycles may vary even for a given pair of vertices. Cyclic reachability is an attribute that decides the overall connectedness of any network. In graph the cycle connectivity (CC) from vertex a to vertex b and from vertex b to vertex a is always one. In fuzzy graph (FG) the CC from vertex a to vertex b and from vertex b to vertex a is always same. But if someone is interested in finding CC from vertex a to an edge ab, then graphs and FGs cannot answer this question. Therefore, in this research article, we proposed the idea of CC for FIG. Because in FIG, we can find CC from vertex a to vertex b and also from vertex a to an edge ab. Also, we proposed the idea of CC of fuzzy incidence cycles (FICs) and complete fuzzy incidence graphs (CFIGs). The fuzzy incidence cyclic cut-vertex, fuzzy incidence cyclic bridge, and fuzzy incidence cyclic cut pair are established. A condition for CFIG to have fuzzy incidence cyclic cut-vertex is examined. Cyclic connectivity index and average cyclic connectivity index of FIG are also investigated. Three different types of vertices, such as cyclic connectivity increasing vertex, cyclically neutral vertex and, cyclic connectivity decreasing vertex, are also defined. The real-life applications of CC of FIG in a highway system of different cities to minimize road accidents and a computer network to find the best computers among all other computers are also provided.
format	article
author	Irfan Nazeer Tabasam Rashid Muhammad Tanveer Hussain
author_facet	Irfan Nazeer Tabasam Rashid Muhammad Tanveer Hussain
author_sort	Irfan Nazeer
title	Cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers.
title_short	Cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers.
title_full	Cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers.
title_fullStr	Cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers.
title_full_unstemmed	Cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers.
title_sort	cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/71727535ed8d4863b463acb557afc874
work_keys_str_mv	AT irfannazeer cyclicconnectivityindexoffuzzyincidencegraphswithapplicationsinthehighwaysystemofdifferentcitiestominimizeroadaccidentsandinanetworkofdifferentcomputers AT tabasamrashid cyclicconnectivityindexoffuzzyincidencegraphswithapplicationsinthehighwaysystemofdifferentcitiestominimizeroadaccidentsandinanetworkofdifferentcomputers AT muhammadtanveerhussain cyclicconnectivityindexoffuzzyincidencegraphswithapplicationsinthehighwaysystemofdifferentcitiestominimizeroadaccidentsandinanetworkofdifferentcomputers
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Cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers.

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