Eccentric Topological Index of the Zero Divisor graph $Γ[\mathbb {Z}_n]$

Abstract: The Zero divisor Graph of a commutative ring $R$, denoted by $\Gamma[R]$, is a graph whose vertices are non-zero zero divisors of $R$ and two vertices are adjacent if their product is zero. 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, elliptical curve and cryptography, physics and statistics. In this paper, we consider the zero divisor graph $\Gamma[\mathbb{Z}{p^n}]$ where $p$ is a prime. We derive the standard form of the Eccentric Connectivity Index, Augmented Eccentric Connectivity Index, and Ediz Eccentric Connectivity Index of the zero divisor graph $\Gamma[\mathbb{Z}{p^n}]$.