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.

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.

Some topological indices in fuzzy graphs

2020 ◽  
Vol 39 (5) ◽  
pp. 6033-6046
Author(s):  
Shriram Kalathian ◽  
Sujatha Ramalingam ◽  
Sundareswaran Raman ◽  
Narasimman Srinivasan
Keyword(s):  
Graph Theory ◽  
Classical Model ◽  
Distance Matrix ◽  
Wiener Index ◽  
Topological Indices ◽  
Fuzzy Graph ◽  
Structural Graph ◽  
Chemical Graph Theory ◽  
Fuzzy Graphs ◽  
Schultz Index

A fuzzy graph is one of the versatile application tools in the field of mathematics, which allows the user to easily describe the fuzzy relation between any objects. The nature of fuzziness is favorable for any environment, which supports to predict the problem and solving it. Fuzzy graphs are beneficial to give more precision and flexibility to the system as compared to the classical model (i.e.,) crisp theory. A topological index is a numerical quantity for the structural graph of the molecule and it can be represented through Graph theory. Moreover, its application not only in the field of chemistry can also be applied in areas including computer science, networking, etc. A lot of topological indices are available in chemical-graph theory and H. Wiener proposed the first index to estimate the boiling point of alkanes called ‘Wiener index’. Many topological indices exist only in the crisp but it’s new to the fuzzy graph environment. The main aim of this paper is to define the topological indices in fuzzy graphs. Here, indices defined in fuzzy graphs are Modified Wiener index, Hyper Wiener index, Schultz index, Gutman index, Zagreb indices, Harmonic index, and Randić index with illustrations. Bounds for some of the indices are proved. The algorithms for distance matrix and MWI are shown. Finally, the application of these indices is discussed.

scholarly journals Wiener Index of Fuzzy Graph by Using Strong Domination

2021 ◽  
pp. 13-24
Author(s):  
Saqr H. AL- Emrany ◽  
Mahiuob M. Q. Shubatah
Keyword(s):  
Domination Number ◽  
Wiener Index ◽  
New Method ◽  
Fuzzy Graph ◽  
Fuzzy Graphs ◽  
The Relationship

Aims/ Objectives: This paper presents a new method to calculate the Wiener index of a fuzzy graph by using strong domination number s of a fuzzy graph G. This method is more useful than other methods because it saves time and eorts and doesn't require more calculations, if the edges number is very larg (n). The Wiener index of some standard fuzzy graphs are investigated. At last, we nd the relationship between strong domination number s and the average (G) of a fuzzy graph G was studied with suitable examples.

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.

scholarly journals On the Wiener Index of the Dot Product Graph over Monogenic Semigroups

2020 ◽  
Vol 13 (5) ◽  
pp. 1231-1240
Author(s):  
Büşra Aydın ◽  
Nihat Akgüneş ◽  
İsmail Naci Cangül
Keyword(s):  
Graph Theory ◽  
Connected Graph ◽  
Molecular Graph ◽  
Wiener Index ◽  
Spectral Graph Theory ◽  
Topological Graph ◽  
Product Graph ◽  
Spectral Graph ◽  
Dot Product ◽  
Sum Of Distances

Algebraic study of graphs is a relatively recent subject which arose in two main streams: One is named as the spectral graph theory and the second one deals with graphs over several algebraic structures. Topological graph indices are widely-used tools in especially molecular graph theory and mathematical chemistry due to their time and money saving applications. The Wiener index is one of these indices which is equal to the sum of distances between all pairs of vertices in a connected graph. The graph over the nite dot product of monogenic semigroups has recently been dened and in this paper, some results on the Wiener index of the dot product graph over monogenic semigroups are given.

scholarly journals Comparing the molecular graph degeneracy of Wiener, Harary, Balaban, Randi´c and ZEP topological indices

2014 ◽  
Vol 23 (2) ◽  
pp. 165-174
Author(s):  
ZOITA-MARIOARA BERINDE ◽  
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Wiener Index ◽  
Topological Indices ◽  
Randić Index ◽  
Discrimination Power ◽  
Harary Index ◽  
Molecular Chemistry ◽  
Randic Index

The aim of this paper is to show that the ZEP topological index has better discrimination power than four well known topological indices in molecular chemistry: Balaban index, Harary index, Randic index, and Wiener index.

scholarly journals The Kirchhoff Index of Toroidal Meshes and Variant Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jia-Bao Liu ◽  
Xiang-Feng Pan ◽  
Jinde Cao ◽  
Xia Huang
Keyword(s):  
Asymptotic Behavior ◽  
Graph Theory ◽  
Distance Function ◽  
Network Theory ◽  
Spectral Graph Theory ◽  
Electrical Network ◽  
Kirchhoff Index ◽  
Resistance Distance ◽  
Spectral Graph ◽  
Explicit Formulae

The resistance distance is a novel distance function on electrical network theory proposed by Klein and Randić. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices inG. In this paper, we established the relationships between the toroidal meshes networkTm×nand its variant networks in terms of the Kirchhoff index via spectral graph theory. Moreover, the explicit formulae for the Kirchhoff indexes ofL(Tm×n),S(Tm×n),T(Tm×n), andC(Tm×n)were proposed, respectively. Finally, the asymptotic behavior of Kirchhoff indexes in those networks is obtained by utilizing the applications of analysis approach.

scholarly journals Wiener Index of Some Operations on Fuzzy Graphs

2021 ◽  
pp. 1-11
Author(s):  
Saqr H. Al-Emrany ◽  
Mahiuob M. Q. Shubatah ◽  
Abdullah Q. Al-Mekhlafi
Keyword(s):  
Cartesian Product ◽  
Wiener Index ◽  
Fuzzy Graph ◽  
Product Composition ◽  
Fuzzy Graphs

In this paper, the concept of the Wiener index in some operations on fuzzy graphs was introduced and investigated. The bound of W(G) of some operations on fuzzy graphs are obtained like union, join, Cartesian product, composition, complete fuzzy graph, and bipartite complete fuzzy graph.

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.

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