on trees attaining an upper bound on the total domination number
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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.
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Journal title:
bulletin of the iranian mathematical societyجلد ۴۱، شماره ۶، صفحات ۱۳۳۹-۱۳۴۴
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