Journal of Combinatorial Optimization

, Volume 33, Issue 2, pp 713–725 | Cite as

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 

Mathematics Subject Classification

05C69 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • A. Bahremandpour
    • 1
  • S. M. Sheikholeslami
    • 1
  • L. Volkmann
    • 2
  1. 1.Department of MathematicsAzarbaijan Shahid Madani UniversityTabrizIslamic Republic of Iran
  2. 2.Lehrstuhl II für MathematikRWTH Aachen UniversityAachenGermany

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