The outer-connected vertex edge domination number of a tree
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For a given graph $G = (V,E)$, a set $D\subseteq V(G)$ is said to be an outer-connected vertex edge dominating set if $D$ is a vertex edge dominating set and the graph $G \setminus D$ is connected. The outer-connected vertex edge domination number of a graph $G$, denoted by $\gamma _{ve} ^{oc}(G)$, is the cardinality of a minimum outer connected vertex edge dominating set of $G$. We characterize trees $T$ of order $n$ with $l$ leaves, $s$ support vertices, for which $\gamma_{ve}^{oc}(T) = (n-l+s+1)/3$ and also characterize trees with equal domination number and outer-connected vertex edge domination number.
Abstract
For a given graph $G = (V,E)$, a set $D\subseteq V(G)$ is said to be an outer-connected vertex edge dominating set if $D$ is a vertex edge dominating set and the graph $G \setminus D$ is connected. The outer-connected vertex edge domination number of a graph $G$, denoted by $\gamma _{ve} ^{oc}(G)$, is the cardinality of a minimum outer connected vertex edge dominating set of $G$. We characterize trees $T$ of order $n$ with $l$ leaves, $s$ support vertices, for which $\gamma_{ve}^{oc}(T) = (n-l+s+1)/3$ and also characterize trees with equal domination number and outer-connected vertex edge domination number.
참고문헌 (6)
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