On trees attaining an upper bound on the total domination number
نویسنده
چکیده مقاله:
A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$. The total domination number of a graph $G$, denoted by $gamma_t(G)$, is~the minimum cardinality of a total dominating set of $G$. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International ournal of Graphs and Combinatorics 1 (2004), 69--75] established the following upper bound on the total domination number of a tree in terms of the order and the number of support vertices, $gamma_t(T) le (n+s)/2$. We characterize all trees attaining this upper bound.
منابع مشابه
on trees attaining an upper bound on the total domination number
a total dominating set of a graph $g$ is a set $d$ of vertices of $g$ such that every vertex of $g$ has a neighbor in $d$. the total domination number of a graph $g$, denoted by $gamma_t(g)$, is~the minimum cardinality of a total dominating set of $g$. chellali and haynes [total and paired-domination numbers of a tree, akce international ournal of graphs and combinatorics 1 (2004), 6...
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عنوان ژورنال
دوره 41 شماره 6
صفحات 1339- 1344
تاریخ انتشار 2015-12-01
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