Connectivity and Wiener Index of Fuzzy Incidence Graphs

Fang, Juanyan; Nazeer, Irfan; Rashid, Tabasam; Liu, Jia‐Bao

doi:10.1155/2021/6682966

Cited by 17 publications

(8 citation statements)

References 29 publications

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“…Malik et al [ 12 ] examined complementary FIGs. Fang et al [ 10 ] presented the connectivity index and Wiener index in FIGs. They also defined different kinds of vertices.…”

Section: Introductionmentioning

confidence: 99%

Connectivity Concepts in Intuitionistic Fuzzy Incidence Graphs with Application

Nazeer

Rashid

2022

Int. J. Appl. Comput. Math

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In this research article, we presented the idea of intuitionistic fuzzy incidence graphs (IFIGs) along with connectivity concepts. IFIGs are the generalization of fuzzy incidence graphs (FIGs). Specific ideas analogous to intuitionistic fuzzy cut-vertices and intuitionistic fuzzy bridges in intuitionistic fuzzy graphs, intuitionistic incidence cut-vertices, and intuitionistic incidence bridges are explored. The notion of intuitionistic incidence gain and intuitionistic incidence loss for intuitionistic incidence paths and pairs of vertices is also initiated. In the case of FIGs, we have only membership value, and we do not have non-membership value (NMSV). Therefore, we use IFIGs because they are more reliable, valuable, and helpful than FIGs. Also, we can not apply graphs, fuzzy graphs, and FIGs to the application provided in Sect. 3 due to the non-availability of NMSV. An application in selecting the best paint company for investment among different companies by using IFIG is also obtained.

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“…Malik et al [ 12 ] examined complementary FIGs. Fang et al [ 10 ] presented the connectivity index and Wiener index in FIGs. They also defined different kinds of vertices.…”

Section: Introductionmentioning

confidence: 99%

Connectivity Concepts in Intuitionistic Fuzzy Incidence Graphs with Application

Nazeer

Rashid

2022

Int. J. Appl. Comput. Math

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“…is the distance between vertices a and b in G. Since the Wiener index was successfully introduced into graph theory, many scholars have done a lot of research on it. is paper is mainly interested in the Wiener index of direct product graphs (to know further about Wiener index of product graphs and other graphs, refer to [7][8][9][10]).…”

Section: Introductionmentioning

confidence: 99%

Exact Wiener Index of the Direct Product of a Path and a Wheel Graph

Duan

2022

Mathematical Problems in Engineering

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The direct product is one of the most important methods to construct large-scale graphs using existing small-scale graphs, and the topological structure parameters of the constructed large-scale graphs can be derived from small-scale graphs. For a simple undirected graph G , its Wiener index W G is defined as the sum of the distances between all different unordered pairs of vertices in the graph. Path is one of the most common and useful graphs, and it is found in almost all virtual and real networks; wheel graph is a kind of graph with good properties and convenient construction. In this paper, the exact value of the Wiener index of the direct product of a path and a wheel graph is given, and the obtained Wiener index is only derived from the orders of the two factor graphs.

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“…e idea of cut-pairs, fuzzy incidence trees, and strong pairs in FIGs was proposed by Mathew and Mordeson [29]. Fang et al [30] presented an idea to find the connectivity and Wiener index of FIG.…”

Section: Introductionmentioning

confidence: 99%

An Application of Product of Intuitionistic Fuzzy Incidence Graphs in Textile Industry

2021

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In this research article, we presented the idea of intuitionistic fuzzy incidence graphs (IFIGs) along with their certain properties. The number of operations including Cartesian product (CP), composition, tensor product, and normal product in an IFIGs are also investigated. The method to compute the degree of IFIGs obtained by CP, composition, tensor product, and the normal product is discussed. Some important theorems to calculate the degree of the vertices of IFIGs acquired by CP, composition, tensor product, and normal product are elaborated. An application of CP and composition of two IFIGs in the textile industry to find the best combinations of departments expressing the highest percentage of progress and the lowest percentage of nonprogress is provided. A comparative analysis of our study with the existing study is discussed. Our study will be beneficial to comprehend and understand the further characteristics of IFIGs in detail. Another advantage of our study is that it will be helpful to find the maximum percentage of progress and minimum percentage of nonprogress in different departments of universities, garment factories, and hospitals.

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Connectivity and Wiener Index of Fuzzy Incidence Graphs

Abstract: Connectivity is a key theory in fuzzy incidence graphs FIGs . In this paper, we introduced connectivity index CI , av… Show more

Cited by 17 publications

References 29 publications

Connectivity Concepts in Intuitionistic Fuzzy Incidence Graphs with Application

Connectivity Concepts in Intuitionistic Fuzzy Incidence Graphs with Application

Exact Wiener Index of the Direct Product of a Path and a Wheel Graph

An Application of Product of Intuitionistic Fuzzy Incidence Graphs in Textile Industry

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