%0 Journal Article
%T On trees attaining an upper bound on the total domination number
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Krzywkowski, M.
%D 2015
%\ 12/01/2015
%V 41
%N 6
%P 1339-1344
%! On trees attaining an upper bound on the total domination number
%K Domination
%K total domination
%K tree
%R
%X 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.
%U http://bims.iranjournals.ir/article_696_4449325767526406edbfafc623313f35.pdf