Bipolar Picture Fuzzy Graphs with Application

Khan, Waheed Ahmad; Ali, Babir; Taouti, Abdelghani

doi:10.3390/sym13081427

Cited by 16 publications

(14 citation statements)

References 29 publications

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“…SovanSamanta [30] discussed some result of bipolar fuzzy graph. Sunitha M. S. and Vijaya Kumar A. discussed the concept of characterization of fuzzy trees [29].Waheed Ahmed Khan, Babir Ali and Abdelghani Taouti [31] introduced and discussed the term bipolar picture fuzzy graph along with some of its fundamental characteristics and applications. Ghorai Ganesh and Pal [11] [12]described various properties of m-polar fuzzy graph and they also examined isomorphic properties of m-polar fuzzy graph.…”

Section: Literature Reviewmentioning

confidence: 99%

A New Approach on Bipolar Second Degree Perfect Fuzzy Matching for Bipolar Fuzzy Graphs Based on Vertices

J. Anusha, Dr. B. Uma Devi, R. K. Shanmugha Priya

2023

tjjpt

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Graph is a visual representation of data. In mathematics, graph is a structure which creates the pairwise relation between objects. The objects are known as nodes or vertices and the connection between two nodes are known as links or edges. A graph is a symmetric binary relation on a non-empty set whereas Fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. Bipolar Fuzzy graph is a generalization of graph theory by using bipolar Fuzzy set. The bipolar Fuzzy sets are the extension of Fuzzy sets. Our main objective is to introduce Bipolar Second Degree Perfect Fuzzy Matching for Bipolar Fuzzy Graph based on vertices. Secondly, we proved the necessary conditions under which they are equivalent and also proved that for a particular condition a perfect second-degree fuzzy matching is not a regular bipolar fuzzy graph. Next, we discussed about perfect second-degree Fuzzy matching and second degree fuzzy matching number for bipolar fuzzy graph on the cycle.

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Section: Literature Reviewmentioning

confidence: 99%

A New Approach on Bipolar Second Degree Perfect Fuzzy Matching for Bipolar Fuzzy Graphs Based on Vertices

J. Anusha, Dr. B. Uma Devi, R. K. Shanmugha Priya

2023

tjjpt

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“…are helpful to analyze the performance of a social network. (27)(28)(29) Since PPFG model has four or more attribute values associated with vertices, a better prediction about the quality of Pvertices possible in PPFG model. The computation of the attribute values for the P-edges in PPFG model reduces the error to the minimum in our prediction regarding strength of connectivity.…”

Section: Application Of Plithogenic Product Fuzzy Graph In Social Networkmentioning

confidence: 99%

A Study on Plithogenic Product Fuzzy Graphs with Application in Social network

Bharathi¹

2021

IJST

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Objectives:The main objective of this study is to define Plithogenic product fuzzy graphs (PPFGs), and introduce its properties. Method: PPFGs is newly introduced as a new graphical model where P-vertices are characterized by four or more attributes and the attribute values of P-edges are computed using the product operator. Findings: Theoretical discussions and results related to PPFGs, and subgraphs, paths, cycles, trees, bridge and cut vertex in PPFGs are demonstrated with examples. A social network model based on the notion of PPFGs has been presented and analyzed to show the utility and the advantage of Plithogenic product fuzzy graph model. Novelty: Strong and weak P-vertices, and highly strong, strong and weak P-edges are identified to analyze the strength of connectivity between different units. P-order, P-size, P-vertex range, P-edge range, degree, total degree, and average P-weight of P-vertices are computed to examine proximity, significance and centrality of units.

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“…Recently, the further extensions of PFGs like constant picture fuzzy graphs [26] and balanced picture fuzzy graphs [27] are also introduced. First and third authors (with Babir Ali) have introduced the notion of bipolar picture fuzzy graphs and bipolar picture fuzzy acquaintanceship graph in [28]. Similarly, the term interval-valued picture fuzzy graphs is explored by both the authors in [29].…”

Section: Introductionmentioning

confidence: 99%

Cayley Picture Fuzzy Graphs and Interconnected Networks

Khan¹,

Faiz²,

Taouti³

2023

Intelligent Automation &Amp; Soft Computing

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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 generalizations 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 ¼ ðC; DÞ defined on a H Ã = ðA; BÞ, where C = ð C ; C ; # C Þ is a picture fuzzy set on A and D = ð D ; D ; # D Þ is a picture fuzzy set over the set B A Â A such that for any edge mn 2 B with D ðm; nÞ minð C ðmÞ; C ðnÞÞ, D ðm; nÞ minð C ðmÞ; C ðnÞÞ and # D ðm; nÞ ! maxð# C ðmÞ; # C ðnÞÞ: 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 characteristics 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.

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Bipolar Picture Fuzzy Graphs with Application

Cited by 16 publications

References 29 publications

A New Approach on Bipolar Second Degree Perfect Fuzzy Matching for Bipolar Fuzzy Graphs Based on Vertices

A New Approach on Bipolar Second Degree Perfect Fuzzy Matching for Bipolar Fuzzy Graphs Based on Vertices

A Study on Plithogenic Product Fuzzy Graphs with Application in Social network

Cayley Picture Fuzzy Graphs and Interconnected Networks

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