This article is cited in 2 papers

Domination and edge domination in trees

B. Senthilkumar, Ya. B. Venkatakrishnan, N. Kumar

SASTRA Deemed University

Abstract: 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.

Language: English

DOI: 10.15826/umj.2020.1.012

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