The Order Gcd Graph

In this paper we define a simple undirected graph Og(Zn) whose vertices are all the elements of Zn and two distinct vertices a, b are adjacent if and only if gcd (O(a), O(b))= O(a·b) . We introduced that the graph Og(Zn) is complete graph for n=pq . where p, q are distinct prime. The graph Og(Zn) is not planar for n= p2 and n= 2k p. where, p is any odd prime and k > 1 . Also, discuss about Eulerian property of the graph and find degree of vertices and clique number of the graph.