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Abstract
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TheRomangamedomination number of an undirected graphG is defined by
the following game. Players A and D orient the edges of the graph G alternately, with
D playing first, until all edges are oriented. Player D (frequently called Dominator)
tries to minimize the Roman domination number of the resulting digraph, while player
A (Avoider) tries to maximize it. This game gives a unique number depending only
on G, if we suppose that both A and D play according to their optimal strategies.
This number is called the Roman game domination number of G and is denoted by
γRg(G). In this paper we initiate the study of the Roman game domination number
of a graph and we establish some bounds on γRg(G). We also determine the Roman
game domination number for some classes of graphs.
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