Rainbow game domination subdivision number of a graph
نویسنده
چکیده
The rainbow 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 2-rainbow dominating number γr2(G ′) of G′ while A tries to maximize it. If both A and D play according to their optimal strategies, γr2(G ′) is well defined. We call this number the rainbow game domination subdivision number of G and denote it by γrg(G). In this paper we initiate the study of the rainbow game domination subdivision number of a graph and present sharp bounds on the rainbow game domination subdivision number of a tree.
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