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

Kashif Elahi, Ali Ahmad and Roslan Hasni
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Kashif Elahi: Deanship of E-learning and Information Technology, Jazan University, Jazan 45142, Saudi Arabia
Ali Ahmad: College of Computer Science and Information Technology, Jazan University, Jazan 45142, Saudi Arabia
Roslan Hasni: Department of Mathematics, University Malaysia Terengganu, Kuala Terengganu 21030, Terengganu, Malaysia

Mathematics, 2018, vol. 6, issue 12, 1-9

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 .

Keywords: topological index; zero divisor graphs; commutative ring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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