Periodica Mathematica Hungarica

, Volume 65, Issue 1, pp 125–134 | Cite as

Nordhaus-Gaddum results for the convex domination number of a graph

  • M. Lemańska
  • J. A. Rodríguez-Velázquez
  • I. Gonzalez Yero


The distance d G (u, v) between two vertices u and v in a connected graph G is the length of the shortest uv-path in G. A uv-path of length d G (u, v) is called a uv-geodesic. A set X is convex in G if vertices from all ab-geodesics belong to X for any two vertices a, bX. The convex domination number γcon(G) of a graph G equals the minimum cardinality of a convex dominating set. In the paper, Nordhaus-Gaddum-type results for the convex domination number are studied.

Key words and phrases

convex domination number Nordhaus-Gaddum results 

Mathematics subject classification numbers

05C05 05C69 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012

Authors and Affiliations

  • M. Lemańska
    • 1
  • J. A. Rodríguez-Velázquez
    • 2
  • I. Gonzalez Yero
    • 2
  1. 1.Department of Technical Physics and Applied MathematicsGdańsk University of TechnologyGdańskPoland
  2. 2.Departament d’Enginyeria Informàtica i MatemàtiquesUniversitat Rovira i VirgiliTarragonaSpain

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