The order difference interval graph of a group

In this paper we introduce the concept of order diference interval graph lceil odi(g) of a group g. it is a graph lceil odi (g) with v ( lceil odi (g)) = g and two vertices a and b are adjacent in lceil odi (g) if and only if o(b) - o(a) ε [o(a), o(b)]. without loss of generality, we assume that o(a) leq o(b). in this paper we obtain several properties of lceil odi (g), upper bounds on the number of edges of lceil odi (g) and determine those groups whose order diference interval graph is isomorphic to a complete multipartite graph