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

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 $${\mathbb{Z}}_{p_1{p}_2}\times {\mathbb{Z}}_q$$, 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 $${\mathbb{Z}}_{p_1{p}_2}\times {\mathbb{Z}}_q$$.