On degree-based entropy measure for zero-divisor graphs

Abstract

Let [Formula: see text] be a commutative ring with [Formula: see text] A zero-divisor graph [Formula: see text] is an undirected graph on the vertex set [Formula: see text] such that any two nonzero elements [Formula: see text] are adjacent whenever [Formula: see text] The concept of entropy measure is fundamental and has been the subject of interest in various fields. The purpose of this paper is to calculate the entropy measure of [Formula: see text] for various rings. We take into consideration the ring [Formula: see text] for [Formula: see text] where [Formula: see text] and [Formula: see text] are distinct prime numbers. Moreover, we also discussed the entropy measure of the zero-divisor graph for the rings [Formula: see text] and [Formula: see text] This study will help us further understand the algebraic structure of the commutative rings.