Edge Regular Property of Cartesian Product and Composition of Two Fuzzy Graphs

2016 ◽  
Vol 6 (2) ◽  
pp. 21
Author(s):  
K. Radha ◽  
Natesan Kumaravel
Keyword(s):  
Cartesian Product ◽  
Fuzzy Graphs ◽  
Regular Property

scholarly journals Multiple Attribute Decision-Making Problem Using Picture Fuzzy Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Sk. Amanathulla ◽  
G. Muhiuddin ◽  
D. Al-Kadi ◽  
M. Pal
Keyword(s):  
Decision Making ◽  
Cartesian Product ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Environment ◽  
Fuzzy Graphs ◽  
Determination Process ◽  
Multiple Attribute ◽  
Picture Fuzzy Set ◽  
Almost All ◽  
The Relationship

In a picture fuzzy environment, almost all multiple attribute decision-making ( MADM ) methods have been discussed a type of problem in which there is no relationship among the attributes. Although the relationship among the attributes should be considered in the actual applications, so we need to pay attention to that important issue. This article applied graph theory to the picture fuzzy set ( PFS ) and obtained a new method, MADM , to solve complicated problems under a picture fuzzy environment. The developed method can capture the relationship among the attributes that cannot be handled well by any existing methods. This study introduces union, intersection, sum, Cartesian product, the composition of picture fuzzy graphs ( PFG s), and their important properties. Finally, by considering the importance of relationships among attributes in the determination process, two algorithms, based on PFG , have developed to solve complicated problems using picture fuzzy information. Also, two numerical examples have introduced to explain how to deal with the MADM problem under picture fuzzy environment.

On construction of fuzzy chromatic number of cartesian product of path and other fuzzy graphs

2020 ◽  
Vol 39 (1) ◽  
pp. 1073-1080
Author(s):  
Isnaini Rosyida ◽  
Widodo ◽  
Ch. Rini Indrati ◽  
Diari Indriati
Keyword(s):  
Chromatic Number ◽  
Cartesian Product ◽  
Fuzzy Graphs

scholarly journals Dominating Energy of Operations on Intuitionistic Fuzzy Graphs

2018 ◽  
Vol 7 (4.10) ◽  
pp. 328 ◽  
Author(s):  
A. Kalimulla ◽  
R. Vijayaragavan ◽  
S. Sharief Basha
Keyword(s):  
Cartesian Product ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Intuitionistic Fuzzy Graphs

The concept of energy of an Intuitionistic Fuzzy Graph is extended to dominating Energy in operations on Intuitionistic Fuzzy Graph. In this paper, We have obtained the value of dominating Energy in different operations such as complement, Union, Join, Cartesian product and composition between two intuitionistic Fuzzy graphs. Also we study the relation between the dominating Energy in the operations on two Intuitionistic Fuzzy Graphs.  

DOMINATION IN PRODUCTS OF FUZZY GRAPHS

2005 ◽  
Vol 13 (02) ◽  
pp. 195-204 ◽  
Author(s):  
A. SOMASUNDARAM
Keyword(s):  
Cartesian Product ◽  
Fuzzy Graphs

In this paper we discuss several operations on fuzzy graphs such as union, join, composition, Cartesian product and study their domination parameters.

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.

ON FUZZY CHROMATIC NUMBER OF CARTESIAN PRODUCT OF SOME FUZZY GRAPHS AND ITS APPLICATION

2019 ◽  
Vol 20 (2) ◽  
pp. 237-252
Author(s):  
Isnaini Rosyida ◽  
Rosyida ◽  
Ch. Rini Indrati ◽  
Diari Indriati
Keyword(s):  
Chromatic Number ◽  
Cartesian Product ◽  
Fuzzy Graphs

scholarly journals New Concepts of Picture Fuzzy Graphs with Application

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 470 ◽  
Author(s):  
Cen Zuo ◽  
Anita Pal ◽  
Arindam Dey
Keyword(s):  
Fuzzy Set ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Strong Product ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Picture Fuzzy Set

The picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, in which a intuitionistic fuzzy set may fail to reveal satisfactory results. Picture fuzzy set is an extension of the classical fuzzy set and intuitionistic fuzzy set. It can work very efficiently in uncertain scenarios which involve more answers to these type: yes, no, abstain and refusal. In this paper, we introduce the idea of the picture fuzzy graph based on the picture fuzzy relation. Some types of picture fuzzy graph such as a regular picture fuzzy graph, strong picture fuzzy graph, complete picture fuzzy graph, and complement picture fuzzy graph are introduced and some properties are also described. The idea of an isomorphic picture fuzzy graph is also introduced in this paper. We also define six operations such as Cartesian product, composition, join, direct product, lexicographic and strong product on picture fuzzy graph. Finally, we describe the utility of the picture fuzzy graph and its application in a social network.

scholarly journals Decision Making Approach under Pythagorean Dombi Fuzzy Graphs for Selection of Leading Textile Industry

2019 ◽  
Vol 24 (4) ◽  
pp. 102
Author(s):  
Muhammad Akram ◽  
Jawaria Mohsan Dar ◽  
Sundas Shahzadi
Keyword(s):  
Decision Making ◽  
Textile Industry ◽  
Research Study ◽  
Cartesian Product ◽  
Multi Criteria Decision Making ◽  
Fuzzy Graph ◽  
Operational Parameter ◽  
Strong Product ◽  
Fuzzy Graphs ◽  
Selection Of

Graphs play a pivotal role in structuring real-world scenarios such as network security and expert systems. Numerous extensions of graph theoretical conceptions have been established for modeling uncertainty in graphical network situations. The Pythagorean Dombi fuzzy graph (PDFG), a generalization of the fuzzy Dombi graph (FDG), is very useful in representing vague relations between several objects, whereas the operational parameter has a flexible nature in decision-making problems. The main objective of this research study is to expand the area of discussion on PDFGs by establishing fruitful results and notions related to operations such as the direct product, Cartesian product, semi-strong product, strong product, and composition on PDFGs. Certain concepts, including the degree of vertices and total degree, are discussed as its modifications. Meanwhile, these outcomes are considered on PDFGs maintaining the strongness property. At the end, an algorithm for Pythagorean Dombi fuzzy multi-criteria decision-making is given, and a numerical example based on the selection of a leading textile industry is put forward to clarify the suitability of the proposed approach.

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