Total domination subdivision number

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Total dominator chromatic number of k-subdivision of graphs

The Art of Discrete and Applied Mathematics, 2022
Let $G$ be a simple graph. A total dominator coloring of $G$, is a proper coloring of the vertices of $G$ in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic (TDC) number $ _d^t(G)$ of $G$, is the minimum number of colors among all total dominator coloring of $G$. For any $k \in \mathbb{N}$,
Alikhani, Saeid, Ghanbari, Nima, Soltani, Samaneh +2 more
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Total domination subdivision numbers of trees

Discrete Mathematics, 2004
The total domination subdivision number $\text{ sd}_{\gamma_t}(G)$ of a graph $G$ is the minimum number of edges whose subdivision increases the total domination number ${\gamma_t}(G)$ of $G$. \textit{T. W. Haynes} et al. [J. Comb. Math. Comb. Comput.
Haynes, Teresa W., Henning, Michael A., Hopkins, Lora +2 more
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Total domination subdivision numbers of graphs

Discussiones Mathematicae Graph Theory, 2004
Summary: A set $S$ of vertices in a graph $G=(V,E)$ is a total dominating set of $G$ if every vertex of $V$ is adjacent to a vertex in $S$. The total domination number of $G$ is the minimum cardinality of a total dominating set of $G$. The total domination subdivision number of $G$ is the minimum number of edges that must be subdivided (
Michael A. Henning, Lora Shuler Hopkins, Teresa W. Haynes +2 more
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On total domination subdivision numbers of trees