Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices

Kashif Elahi,Roslan Hasni,Ali Ahmad

doi:10.3390/math6120301

Kashif Elahi, Roslan Hasni + Show 1 more

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https://doi.org/10.3390/math6120301

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Journal: Mathematics	Publication Date: Dec 4, 2018
Citations: 18	License type: CC BY 4.0

Affiliation: Jazan University, Universiti Malaysia Terengganu

Abstract

Chemical graph theory is a branch of mathematical chemistry which deals with the non-trivial applications of graph theory to solve molecular problems. Graphs containing finite commutative rings also have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this paper we discuss eccentric topological indices of zero divisor graphs of commutative rings Z p 1 p 2 × Z q , where p 1 , p 2 , and q are primes. To enhance the importance of these indices a construction algorithm is also devised for zero divisor graphs of commutative rings Z p 1 p 2 × Z q .

Highlights

A single number that can be utilized to depict properties of the graph of a molecule is known as a topological descriptor for that graph
Topological descriptors are utilized within the improvement of quantitative structure-activity connections (QSARs) and quantitative structure-property connections (QSPR) in which the organic movement or other properties of atoms are connected with their chemical structure
Topological descriptors are utilized in QSPR/QSAR. These days, there exists a variety of topological descriptors that have some applications in chemistry, physics, robotics, statistics, and computer networks

Summary

Introduction

A single number that can be utilized to depict properties of the graph of a molecule is known as a topological descriptor for that graph. There are different topological descriptors that have found a number of applications in theoretical science. Topological descriptors are utilized within the improvement of quantitative structure-activity connections (QSARs) and quantitative structure-property connections (QSPR) in which the organic movement or other properties of atoms are connected with their chemical structure. These days, there exists a variety of topological descriptors that have some applications in chemistry, physics, robotics, statistics, and computer networks. The topological descriptors deal with the distance among the vertices in a graph are “distance-based topological indices”. Other topological descriptors that deal with the degree of vertices in graph are “degree-based topological indices”

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