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.