Geodesic
Domination and edge domination in trees
Ural mathematical journal, Tome 6 (2020) no. 1, pp. 147-152

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Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ is a dominating set if every vertex in $V \setminus S$ is adjacent to a vertex in $S$. The domination number of a graph $G$, denoted by $\gamma(G)$ is the minimum cardinality of a dominating set of $G$. A set $D \subseteq E$ is an edge dominating set if every edge in $E\setminus D$ is adjacent to an edge in $D$. The edge domination number of a graph $G$, denoted by $\gamma'(G)$ is the minimum cardinality of an edge dominating set of $G$. We characterize trees with domination number equal to twice edge domination number.
Keywords: Edge dominating set, Dominating set, Trees. 
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B. Senthilkumar; Ya. B. Venkatakrishnan; N. Kumar. Domination and edge domination in trees. Ural mathematical journal, Tome 6 (2020) no. 1, pp. 147-152. http://geodesic.mathdoc.fr/item/UMJ_2020_6_1_a11/