Energy and Wiener index of divisor graph of commutative ring

Abstract

In recent paper, P. D. Khandare et al. introduced a graphical structure of non empty finite ring R called as divisor graph ⅅ[R] and discussed some properties of the graph ⅅ[Zn]. In this article, we will continue the study of the divisor graph ⅅ[Zn] and discuss some more properties of ⅅ[Zn]. If n ∈ N then we derive general formula for total degree and stability number of ⅅ[Zn]. Moreover we find adjacency matrix of the graph ⅅ[Zn] and derived formula for energy of ⅅ[Zn] when n = pk, k ∈ N and n = pq, for primes p and q.