@article {
author = {Krzywkowski, M.},
title = {On trees attaining an upper bound on the total domination number},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {41},
number = {6},
pages = {1339-1344},
year = {2015},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {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. },
keywords = {Domination,total domination,tree},
url = {http://bims.iranjournals.ir/article_696.html},
eprint = {http://bims.iranjournals.ir/article_696_4449325767526406edbfafc623313f35.pdf}
}