Information Processing Letters
Paired-Domination in Claw-Free Cubic Graphs
Graphs and Combinatorics
Paired-Domination in P 5-Free Graphs
Graphs and Combinatorics
Paired-Domination in Subdivided Star-Free Graphs
Graphs and Combinatorics
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A vertex in G is said to dominate itself and its neighbors. A subset S of vertices is a dominating set if S dominates every vertex of G. A paired-dominating set is a dominating set whose induced subgraph contains a perfect matching. The paired-domination number of a graph G, denoted by 驴 pr(G), is the minimum cardinality of a paired-dominating set in G. A subset S⊆V(G) is a double dominating set of G if S dominates every vertex of G at least twice. The minimum cardinality of a double dominating set of G is the double domination number 驴 脳2(G). A claw-free graph is a graph that does not contain K 1,3 as an induced subgraph. Chellali and Haynes (Util. Math. 67:161---171, 2005) showed that for every claw-free graph G, we have 驴 pr(G)≤驴 脳2(G). In this paper we extend this result by showing that for r驴2, if G is a connected graph that does not contain K 1,r as an induced subgraph, then $\gamma_{\mathrm{pr}}(G)\le ( \frac{2r^{2}-6r+6}{r(r-1)} )\gamma_{\times2}(G)$ .