scholarly journals Generalized Fuzzy Graph Connectivity Parameters with Application to Human Trafficking

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 424
Author(s):  
Arya Sebastian ◽  
John N Mordeson ◽  
Sunil Mathew
Keyword(s):  
Human Trafficking ◽  
Network Theory ◽  
Graph Connectivity ◽  
Fuzzy Graph ◽  
Graph Models ◽  
Edge Connectivity ◽  
Clustering Techniques ◽  
New Class ◽  
Large Size ◽  
Fuzzy Graphs

Graph models are fundamental in network theory. But normalization of weights are necessary to deal with large size networks like internet. Most of the research works available in the literature have been restricted to an algorithmic perspective alone. Not much have been studied theoretically on connectivity of normalized networks. Fuzzy graph theory answers to most of the problems in this area. Although the concept of connectivity in fuzzy graphs has been widely studied, one cannot find proper generalizations of connectivity parameters of unweighted graphs. Generalizations for some of the existing vertex and edge connectivity parameters in graphs are attempted in this article. New parameters are compared with the old ones and generalized values are calculated for some of the major classes like cycles and trees in fuzzy graphs. The existence of super fuzzy graphs with higher connectivity values are established for both old and new parameters. The new edge connectivity values for some wider classes of fuzzy graphs are also obtained. The generalizations bring substantial improvements in fuzzy graph clustering techniques and allow a smooth theoretical alignment. Apart from these, a new class of fuzzy graphs called generalized t-connected fuzzy graphs are studied. An algorithm for clustering the vertices of a fuzzy graph and an application related to human trafficking are also proposed.

Vertex Connectivity of Fuzzy Graphs with Applications to Human Trafficking

2018 ◽  
Vol 14 (03) ◽  
pp. 457-485 ◽  
Author(s):  
Shanookha Ali ◽  
Sunil Mathew ◽  
John N. Mordeson ◽  
Hossein Rashmanlou
Keyword(s):  
Real Number ◽  
Human Trafficking ◽  
Dynamic Network ◽  
Arbitrary Real Number ◽  
Fuzzy Graph ◽  
Vertex Connectivity ◽  
The Past ◽  
Fuzzy Graphs ◽  
Number Formula ◽  
Fuzzy Vertex

Connectivity is the most important aspect of a dynamic network. It has been widely studied and applied in different perspectives in the past. In this paper, constructions of [Formula: see text]-connected fuzzy graphs for an arbitrary real number [Formula: see text] and average fuzzy vertex connectivity of fuzzy graphs are discussed. Average fuzzy vertex connectivity of fuzzy trees, fuzzy cycles and complete fuzzy graphs are studied. The concept of a uniformly [Formula: see text]-connected fuzzy graph is introduced and characterized towards the end. An application related to human trafficking is also discussed.

First Zagreb index on a fuzzy graph and its application

2021 ◽  
pp. 1-13
Author(s):  
Sk Rabiul Islam ◽  
Madhumangal Pal
Keyword(s):  
Network Theory ◽  
Cartesian Product ◽  
Spectral Graph Theory ◽  
Fuzzy Graph ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Molecular Chemistry ◽  
Spectral Graph ◽  
Fuzzy Graphs ◽  
A Company

The Zagreb index (ZI) is a very important graph parameter and it is extensively used in molecular chemistry, spectral graph theory, network theory and several fields of mathematics and chemistry. In this article, the first ZI is studied for several fuzzy graphs like path, cycle, star, fuzzy subgraph, etc. and presented an ample number of results. Also, it is established that the complete fuzzy graph has maximal first ZI among n-vertex fuzzy graphs. Some bounds of first ZI are discussed for Cartesian product, composition, union and join of two fuzzy graphs. An algorithm has been designed to calculate the first ZI of a fuzzy graph. At the end of the article, a multi-criteria decision making (MCDM) method is provided using the first ZI of a fuzzy graph to find the best employee in a company. Also a comparison is provided among related indices on the result of application and shown that our method gives better results.

scholarly journals A Study on Connectivity Concepts in Intuitionistic Fuzzy Graphs

2021 ◽  
Vol 16 ◽  
pp. 77-82
Author(s):  
Wael Ahmad Alzoubi ◽  
As’ad Mahmoud As’ad Alnaser
Keyword(s):  
Graph Connectivity ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Intuitionistic Fuzzy Graphs

In this paper, we introduced some concepts of connectivity in an intuitionistic fuzzy graphs, also we study intuitionistic fuzzy cut vertices and intuitionistic fuzzy bridges in fuzzy graph. Connectivity in complete intuitionistic fuzzy graphs is also studied

Hyper-Wiener index for fuzzy graph and its application in share market

2021 ◽  
pp. 1-11
Author(s):  
Sk Rabiul Islam ◽  
Madhumangal Pal
Keyword(s):  
Network Theory ◽  
Spanning Tree ◽  
Wiener Index ◽  
Topological Indices ◽  
Spectral Graph Theory ◽  
Fuzzy Graph ◽  
Molecular Chemistry ◽  
Spectral Graph ◽  
Fuzzy Graphs ◽  
Maximum Spanning Tree

Topological indices have an important role in molecular chemistry, network theory, spectral graph theory and several physical worlds. Most of the topological indices are defined in a crisp graph. As fuzzy graphs are more generalization of crisp graphs, those indices have more application in fuzzy graphs also. In this article, we introduced the fuzzy hyper-Wiener index (FHWI) and studied this index for various fuzzy graphs like path, cycle, star, etc and provided some interesting bounds of FHWI for that fuzzy graph. A lower bound of FHWI is established for n-vertex connected fuzzy graph depending on strength of a strong edges. A relation between FHWI of a tree and its maximum spanning tree is established and this index is calculated for the saturated cycle. Also, at the end of the article, an application in the share market of this index is presented.

Results on Vague Graphs with Applications in Human Trafficking

2018 ◽  
Vol 14 (01) ◽  
pp. 37-52 ◽  
Author(s):  
E. Darabian ◽  
R. A. Borzooei
Keyword(s):  
Human Trafficking ◽  
Fuzzy Graph ◽  
Fuzzy Graphs ◽  
Vague Graph

A vague graph is a generalized structure of a fuzzy graph that gives more precision, exibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, the concepts of eccentricity of nodes, radius and diameter of vague graphs are introduced. The special types of graphs such as eccentrice and antipodal vague graphs are investigated. Then, the relation between eccentrice and antipodal vague graphs are discussed. Finally, an application of eccentrice and antipodal vague graphs in human traffickingn studied.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

On Laplacian energy of picture fuzzy graphs in site selection problem

2021 ◽  
pp. 1-18
Author(s):  
Mahima Poonia ◽  
Rakesh Kumar Bajaj
Keyword(s):  
Decision Making ◽  
Site Selection ◽  
Upper Bounds ◽  
Selection Problem ◽  
Hydropower Plant ◽  
Fuzzy Graph ◽  
Fuzzy Information ◽  
Fuzzy Graphs ◽  
Laplacian Energy ◽  
Selection For

In the present work, the adjacency matrix, the energy and the Laplacian energy for a picture fuzzy graph/directed graph have been introduced along with their lower and the upper bounds. Further, in the selection problem of decision making, a methodology for the ranking of the available alternatives has been presented by utilizing the picture fuzzy graph and its energy/Laplacian energy. For the shake of demonstrating the implementation of the introduced methodology, the task of site selection for the hydropower plant has been carried out as an application. The originality of the introduced approach, comparative remarks, advantageous features and limitations have also been studied in contrast with intuitionistic fuzzy and Pythagorean fuzzy information.

scholarly journals Complement of max product of intuitionistic fuzzy graphs

2021 ◽  
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Hamming Distance ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Degree Of A Vertex ◽  
Intuitionistic Fuzzy Graphs

AbstractIn this paper, the complement of max product of two intuitionistic fuzzy graphs is defined. The degree of a vertex in the complement of max product of intuitionistic fuzzy graph is studied. Some results on complement of max product of two regular intuitionistic fuzzy graphs are stated and proved. Finally, we provide an application of intuitionistic fuzzy graphs in school determination using normalized Hamming distance.

scholarly journals Applications of Fuzzy Graph Theory Portrayed in Various Fields

2021 ◽  
Author(s):  
Abdul Muneera ◽  
T. Nageswara Rao ◽  
R. V. N. Srinivasa ◽  
J. Venkateswara Rao
Keyword(s):  
Graph Theory ◽  
Wireless Sensor Network ◽  
Sensor Network ◽  
Material Science ◽  
Natural Sciences ◽  
Wireless Sensor ◽  
Fuzzy Graph ◽  
Ecological Conditions ◽  
Fuzzy Graphs ◽  
Remote System

Abstract The intend of the paper is to grant the centrality of fuzzy graph (f-graph) hypothetical ideas and the uses of dominations in fuzzy graphs to different genuine circumstances in the territories of science and designing. It is seen an eminent development because of various applications in PC and correspondence, biomedical, atomic material science and science, interpersonal organizations, natural sciences and in different various regions. Interpersonal organizations are the zones where countless individuals are associated. A wireless sensor Network (WSN) remote system which comprises of spatially circulated independent sensors to screen the physical or ecological conditions, for example, pressure, temperature, sound and so forth and to communicate their data through the remote system to a fundamental area. This paper gives an audit of the employments of Fuzzy Graph theory in different sorts of fields.

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