Total restrained domination in claw-free graphs |
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Authors: | Hongxing Jiang Liying Kang |
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Institution: | 1.Department of Mathematics,Shanghai University,Shanghai,China;2.Department of Mathematics,Wenzhou University,Wenzhou,China |
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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. |
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Keywords: | |
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