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Restrained Domination in Claw-Free Graphs with Minimum Degree at Least Two

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Abstract

Let G = (V, E) be a graph. A set \({S\subseteq V}\) is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The restrained domination number of G, denoted γ r (G), is the smallest cardinality of a restrained dominating set of G. We will show that if G is claw-free with minimum degree at least two and \({G\notin \{C_{4},C_{5},C_{7},C_{8},C_{11},C_{14},C_{17}\}}\) , then \({\gamma_{r}(G)\leq \frac{2n}{5}.}\)

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, 30303-3083, USA

    Johannes H. Hattingh

  2. Department of Mathematics, University of Johannesburg, Auckland Park, Johannesburg, 2006, South Africa

    Ernst J. Joubert

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  1. Johannes H. Hattingh
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  2. Ernst J. Joubert
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Correspondence to Johannes H. Hattingh.

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Hattingh, J.H., Joubert, E.J. Restrained Domination in Claw-Free Graphs with Minimum Degree at Least Two. Graphs and Combinatorics 25, 693–706 (2009). https://doi.org/10.1007/s00373-010-0883-3

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  • DOI: https://doi.org/10.1007/s00373-010-0883-3

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