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

  • Authors:

  • Johannes H. Hattingh;Ernst J. Joubert

  • Affiliations:

  • Georgia State University, Department of Mathematics and Statistics, 30303-3083, Atlanta, GA, USA;University of Johannesburg, Department of Mathematics, Auckland Park, 2006, Johannesburg, South Africa

  • Venue:
  • Graphs and Combinatorics
  • Year:
  • 2009

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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 $${\gamma_{r}(G)\leq \frac{2n}{5}.}$$