Restrained Domination in Claw-Free Graphs with Minimum Degree at Least Two |
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Authors: | Johannes H Hattingh Ernst J Joubert |
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Institution: | 1.Department of Mathematics and Statistics,Georgia State University,Atlanta,USA;2.Department of Mathematics,University of Johannesburg,Johannesburg,South Africa |
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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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