Geodesic
On the Total Domination Subdivision Number in Graphs
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 1 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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A set $S\subseteq V$ of vertices in a graph $G=(V,E)$ without isolated vertices is a {\em total dominating set} if every vertex of $V$ is adjacent to some vertex in $S$. The {\em total domination number} $\gamma_t(G)$ is the minimum cardinality of a total dominating set of $G$. The {\em total domination subdivision number} ${\rm sd}_{\gamma_t}(G)$ is the minimum number of edges that must be subdivided (each edge in $G$ can be subdivided at most once) in order to increase the total domination number. In this paper we prove that ${\rm sd}_{\gamma_t}(G)\le \alpha'(G)+1$ for some classes of graphs where $\alpha '(G)$ is the maximum cardinality of a matching of $G$.
Classification : 05C69 
@article{BMMS_2014_37_1_a16,
     author = {O. Favaron and H. Karami and R. Khoeilar and S. M. Sheikholeslami},
     title = {On the {Total} {Domination} {Subdivision} {Number} in {Graphs}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2014},
     volume = {37},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a16/}
}
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O. Favaron; H. Karami; R. Khoeilar; S. M. Sheikholeslami. On the Total Domination Subdivision Number in Graphs. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a16/