مشخصات پژوهش

The game domination subdivision number of a graph G is defined by the following game. Two players D and A, D playing first, alternately mark or subdivide an edge of G which is not yet marked nor subdivided. The game ends when all the edges of G are marked or subdivided and results in a new graph G. The purpose of D is to minimize the domination number γ (G) of G while A tries to maximize it. If bothAand D play according to their optimal strategies, γ (G) is well defined.We call this number the game domination subdivision number of G and denote it by γgs (G). In this paper we initiate the study of the game domination subdivision number of a graph and present sharp bounds on the game domination subdivision number of a tree.