@article{10.5614/ejgta.2016.4.1.10,
author = {M. H. Akhbari and Nader Jafari Rad},
title = {Bounds on Weak and Strong Total Domination in Graphs},
number = {1},
volume = {4},
journal = {Electronic Journal of Graph Theory and Applications},
year = {2016},
abstract = {A set $D$ of vertices in a graph $G=(V,E)$ is a total dominatingset if every vertex of $G$ is adjacent to some vertex in $D$. Atotal dominating set $D$ of $G$ is said to be weak if everyvertex $v\in V-D$ is adjacent to a vertex $u\in D$ such that$d_{G}(v)\geq d_{G}(u)$. The weak total domination number$\gamma_{wt}(G)$ of $G$ is the minimum cardinality of a weaktotal dominating set of $G$. A total dominating set $D$ of $G$ issaid to be strong if every vertex $v\in V-D$ is adjacent to avertex $u\in D$ such that $d_{G}(v)\leq d_{G}(u)$. The strongtotal domination number $\gamma_{st}(G)$ of $G$ is the minimumcardinality of a strong total dominating set of $G$. We presentsome bounds on weak and strong total domination number of a graph.},
doi = {10.5614/ejgta.2016.4.1.10},
pages = {111--118},
}