title: On the characterization of claw-free graphs with given total restrained domination number.
abstract: A setSof vertices in graph [Formula: see text] is a [Formula: see text], abbreviated TRDS, ofGif every vertex ofGis adjacent to a vertex inSand every vertex of [Formula: see text] is adjacent to a vertex in [Formula: see text]. The [Formula: see text] ofG, denoted by [Formula: see text], is the minimum cardinality of a TRDS ofG. Jiang and Kang (J Comb Optim. 19:60-68, 2010) characterized the connected claw-free graphGof ordernwith [Formula: see text]. This paper studies the total restrained domination number of claw-free graphs and characterizes the connected claw-free graphGof ordernwith [Formula: see text].
authors: Department of Mathematics, Harbin Normal University, Harbin, 150025 China.
authors: Xiaoming
authors: X
authors: Pi
keywords: Claw-free graphs; Total restrained dominating set; Total restrained domination number