TY - JOUR
ID - 696
TI - On trees attaining an upper bound on the total domination number
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Krzywkowski, M.
AD - Department of Pure and Applied Mathematics, University of Johannesburg, South Africa \newline Research fellow of the Claude Leon Foundation.
Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Poland.
Y1 - 2015
PY - 2015
VL - 41
IS - 6
SP - 1339
EP - 1344
KW - Domination
KW - total domination
KW - tree
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_696.html
L1 - http://bims.iranjournals.ir/article_696_4449325767526406edbfafc623313f35.pdf
ER -