Randić spectrum of the weakly zero-divisor graph of the ring ℤn

Abstract

In this article, we find the Randić spectrum of the weakly zero-divisor graph of a finite commutative ring R with identity 1 ≠ 0 , denoted as W Γ ( R ) , where R is taken as the ring of integers modulo n . The weakly zero-divisor graph of the ring R is a simple undirected graph with vertices representing non-zero zero-divisors in R . Two vertices, denoted as a and b, are connected if there are elements x in the annihilator of a and y in the annihilator of b such that their product xy equals zero. In particular, we examine the Randić spectrum of W Γ ( Z n ) for specific values of n , which are products of prime numbers and their powers.