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

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Abstract

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, b ∈ X. 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.

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Authors and Affiliations

  1. Department of Technical Physics and Applied Mathematics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80-233, Gdańsk, Poland

    M. Lemańska

  2. Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007, Tarragona, Spain

    J. A. Rodríguez-Velázquez & I. Gonzalez Yero

Authors
  1. M. Lemańska
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  2. J. A. Rodríguez-Velázquez
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  3. I. Gonzalez Yero
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Correspondence to M. Lemańska.

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Communicated by Imre Bárány

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Lemańska, M., Rodríguez-Velázquez, J.A. & Gonzalez Yero, I. Nordhaus-Gaddum results for the convex domination number of a graph. Period Math Hung 65, 125–134 (2012). https://doi.org/10.1007/s10998-012-2174-7

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  • DOI: https://doi.org/10.1007/s10998-012-2174-7

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