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Open AccessArticle

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

by Kashif Elahi 1,2,*, Ali Ahmad 3,* and Roslan Hasni 2,*
1
Deanship of E-learning and Information Technology, Jazan University, Jazan 45142, Saudi Arabia
2
Department of Mathematics, University Malaysia Terengganu, Kuala Terengganu 21030, Terengganu, Malaysia
3
College of Computer Science and Information Technology, Jazan University, Jazan 45142, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Mathematics 2018, 6(12), 301; https://doi.org/10.3390/math6120301
Received: 26 October 2018 / Revised: 30 November 2018 / Accepted: 2 December 2018 / Published: 4 December 2018
(This article belongs to the Special Issue Discrete Optimization: Theory, Algorithms, and Applications)
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 . View Full-Text
Keywords: topological index; zero divisor graphs; commutative ring topological index; zero divisor graphs; commutative ring
MDPI and ACS Style

Elahi, K.; Ahmad, A.; Hasni, R. Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices. Mathematics 2018, 6, 301.

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