Varieties of detour domination number of graphs

Let G = (V,E) be a graph. A u- v a detour is a longest u- v path. A subset DσV is called a detour set of G if every vertex in V-D lie in a detour joining the vertices of D. A subset DσV which is both a detour set and dominating set is called a detour dominating set of G and the cardinality of a minimum detour dominating set is called the detour domination number of G. In this paper, we introduce the concept of different detour domination numbers and find the same for some simple and special graphs.