ON CORONA PRODUCT OF ZERO-DIVISOR GRAPHS OF DIRECT PRODUCT OF FINITE FIELDS

Abstract

The zero-divisor graph of a commutative ring $R$ is defined to be a graph with all the elements of ring $R$ as vertices and two distinct vertices $x, y$ adjacent if and only if $x \cdot y=0$. Thereafter, it got modified by considering only the non-zero zero-divisors as the vertices of the zero-divisor graph denoted by $\Gamma(R)$ and two distinct vertices $x, y$ adjacent if and only if $x \cdot y=0$. The graph generated by taking one copy of $G$, referred to as the centre graph, and $|V(G)|$ copies of $H$, referred to as the outer graph, and making the $i^{\text {th }}$ vertex of $G$ adjacent to every vertex of the $i^{\text {th }}$ copy of $H$ is the Corona product of $G$ and $H(1 \leq i \leq|V(G)|)$ denoted by $G \odot H$. In this paper, we determine the graph properties such as diameter, girth, clique number, vertex chromatic number, and independence number of Corona product of zero-divisor graphs of direct product of finite fields.

Received: February 13, 2023
Accepted: June 28, 2023