Distance related spectrum of the zero-divisor graph on the ring of integers modulo n

Abstract

For a commutative ring R with non-zero identity, let Z ∗ (R) denote the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by Γ(R), is a simple undirected graph with all non-zero zero-divisors as vertices and two distinct vertices x, y ∈ Z ∗ (R) are adjacent if and only if xy = 0. In this paper, the distance, distance Laplacian and the distance singless Laplacian spectrum of Γ(Z n ), for n = p 3 , pq are investigated.