Roman game domination number of a graph

A. Bahremandpour, S. M. Sheikholeslami () and L. Volkmann ()
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A. Bahremandpour: Azarbaijan Shahid Madani University
S. M. Sheikholeslami: Azarbaijan Shahid Madani University
L. Volkmann: RWTH Aachen University

Journal of Combinatorial Optimization, 2017, vol. 33, issue 2, No 20, 713-725

Abstract: Abstract The Roman game domination number of an undirected graph G is defined by the following game. Players $$\mathcal {A}$$ A and $$\mathcal {D}$$ D orient the edges of the graph G alternately, with $$\mathcal {D}$$ D playing first, until all edges are oriented. Player $$\mathcal {D}$$ D (frequently called Dominator) tries to minimize the Roman domination number of the resulting digraph, while player $$\mathcal {A}$$ A (Avoider) tries to maximize it. This game gives a unique number depending only on G, if we suppose that both $$\mathcal {A}$$ A and $$\mathcal {D}$$ D play according to their optimal strategies. This number is called the Roman game domination number of G and is denoted by $$\gamma _{Rg}(G)$$ γ R g ( G ) . In this paper we initiate the study of the Roman game domination number of a graph and we establish some bounds on $$\gamma _{Rg}(G)$$ γ R g ( 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 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0001-4

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