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

Author

Listed:
  • Kashif Elahi

    (Deanship of E-learning and Information Technology, Jazan University, Jazan 45142, Saudi Arabia
    Department of Mathematics, University Malaysia Terengganu, Kuala Terengganu 21030, Terengganu, Malaysia)

  • 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)

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 .

Suggested Citation

  • Kashif Elahi & Ali Ahmad & Roslan Hasni, 2018. "Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices," Mathematics, MDPI, vol. 6(12), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:301-:d:187906
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    References listed on IDEAS

    as
    1. Nadeem, Muhammad Faisal & Zafar, Sohail & Zahid, Zohaib, 2015. "On certain topological indices of the line graph of subdivision graphs," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 790-794.
    2. Nadeem, Muhammad Faisal & Zafar, Sohail & Zahid, Zohaib, 2016. "On topological properties of the line graphs of subdivision graphs of certain nanostructures," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 125-130.
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