Commun. Korean Math. Soc. 2018; 33(1): 361-369
Online first article January 3, 2018 Printed January 31, 2018
https://doi.org/10.4134/CKMS.c150243
Copyright © The Korean Mathematical Society.
Balakrishna Krishnakumari, Yanamandram Balasubramanian Venkatakrishnan
SASTRA University, SASTRA University
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.
Keywords: outer-connected domination, vertex edge domination, outer-connected vertex edge domination, tree
MSC numbers: 05C05, 05C69
2018; 33(2): 631-638
2012; 27(4): 665-668
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