For two vertices u and v in a graph G = (V,E), the detour distance D(u, v) is length of longest − path G. A called detour. subsets B V , D(A,B) defined as min{D(x, y) : x ∈ A, y B}. an A-B joining sets A,B ⊆ where B. vertex said to lie on if some A−B set S E edge-to-vertex every incident with edge or lies pair edges S. The number dn2(G) minimum order its any basis Graphs size q for which 2 are ...