A subset S of V is called an edge detour set of G if every edge in G lies on a detour joining a pair of vertices of S. The edge detour number dn1(G) of G is the minimum order of its edge detour sets and any edge detour set of order dn1 is an edge detour basis. An edge detour dominating set is a subset S of V(G) which is both dominating and an edge detour set of G. The smallest cardinality of an edge detour dominating set of G is called the edge detour domination number of G. In this paper, it is found for the (γ,eD)-number of an edge added graphs of some known graphs such as path, cycle and complete graph.