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.