The order difference interval graph of a group

‎‎In this paper we introduce the concept of order difference interval graph \Gamma_{ODI}(G) of a group G‎. ‎It is a graph \Gamma_{ODI}(G) with V(\Gamma_{ODI}(G)) = G and two vertices a and b are adjacent in \Gamma_{ODI}(G) if and only if o(b)-o(a) \in [o(a)‎, ‎o(b)]‎. ‎Without loss of generality‎, ‎we assume that o(a) \leq o(b)‎. ‎In this paper we obtain several properties of \Gamma_{ODI}(G)‎, ‎upper bounds on the number of edges of \Gamma_{ODI}(G) and determine those groups whose order difference interval graph is isomorphic to a complete multipartite graph‎.

کلیدواژه ها:

Order difference interval graph ، unicyclic graph ، Eulerian ، gen- erating set