Difference divisor graph of the finite group

Let (Z n ,Ꝋ) be a finite group of integers modulo n and Dn a non-empty subset of Z n containing proper devisors of n . In this paper, we have introduced difference divisor graph Dif (Z n , Dn ) associated with Z n whose vertices coincide with Z n such that two distinct vertices are adjacent if and only if either a - b ϵ Dn , or, b - a ϵ Dn . Then we have investigated its algebraic and graph theoretic properties. Further, we have proved that the difference divisor graph Dif (Z n , Dn ) is not a Cayley graph.