On degree-based entropy measure for zero-divisor graphs

Let R be a commutative ring with 1. A zero-divisor graph ∧(R) is an undirected graph on the vertex set R-{0} such that any two nonzero elements p,q ∈ R are adjacent whenever p · q = 0. 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 ∧ (R) for various rings. We take into consideration the ring ℤ_h for h = φ ψ, φ² φ ψ, φ² ψ², φ ψ χ, where φ, ψ and χ are distinct prime numbers. Moreover, we also discussed the entropy measure of the zero-divisor graph for the rings ℤ φ × ℤ ψ, ℤ φ × ℤ ψ ℤ χ, ℤ φ ψ × ℤ χ, and ℤ φ² × ℤ ψ². This study will help us further understand the algebraic structure of the commutative rings.