A set S of vertices in graph G = (V, E) is a total restraineddominatingset, abbreviated 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 totalrestraineddominationnumber of G, denoted by γtr(G), is the minimum cardinality of a TRDS of G. Jiang and Kang (J Comb Optim. 19:60–68, ) characterized the connected claw-free graph G of order n with γtr(G) = n. This paper studies the total restrained domination number of claw-free graphs and characterizes the connected claw-free graph G of order n with γtr(G) = n - 2.
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机译：图G =（V，E）中的一组顶点S是总余弦 n e d d o m i n a t i n g s e t ，缩写TRDS，如果 G 的每个顶点都与 S 中的一个顶点相邻，并且 V - S 与 V - S 中的顶点相邻。 t o t a l r < em> e s t r a i n e d d o m i < / em> n a t i o n > n u m b e r 由γ t r （ G ）表示的 G 是最小基数 G 的TRDS。 Jiang and Kang（J Comb Optim。19：60–68，）描述了具有γ <阶的 n 的连通无爪图 G em> t r （ G ）= n 。本文研究了无爪图的总约束控制数，并刻画了具有γ n 的连通无爪图 G > t r （ G ）= n -2。
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