Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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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.

The outer-connected vertex edge domination number of a tree

Balakrishna Krishnakumari, Yanamandram Balasubramanian Venkatakrishnan

SASTRA University, SASTRA University

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.

Keywords: outer-connected domination, vertex edge domination, outer-connected vertex edge domination, tree

MSC numbers: 05C05, 05C69

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