Journal of Combinatorial Optimization

, Volume 33, Issue 2, pp 713–725

# Roman game domination number of a graph

• A. Bahremandpour
• S. M. Sheikholeslami
• L. Volkmann
Article

## Abstract

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

### Keywords

Domination number Game domination number Roman domination Roman game domination number

05C69

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