Total restrained domination in claw-free graphs

Hongxing Jiang and Liying Kang ()
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Hongxing Jiang: Shanghai University
Liying Kang: Shanghai University

Journal of Combinatorial Optimization, 2010, vol. 19, issue 1, No 5, 60-68

Abstract: Abstract A set S of vertices in a graph G=(V,E) is a total restrained dominating set (TRDS) of G if every vertex of G is adjacent to a vertex in S and every vertex of V−S is adjacent to a vertex in V−S. The total restrained domination number of G, denoted by γ tr (G), is the minimum cardinality of a TRDS of G. In this paper we characterize the claw-free graphs G of order n with γ tr (G)=n. Also, we show that γ tr (G)≤n−Δ+1 if G is a connected claw-free graph of order n≥4 with maximum degree Δ≤n−2 and minimum degree at least 2 and characterize those graphs which achieve this bound.

Keywords: Characterization; Claw-free graphs; Total restrained domination (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10878-008-9161-1

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