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Abstract
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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.
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