A new upper bound on the global defensive alliance number in trees
type: Item
instance of: scholarly article
title: A new upper bound on the global defensive alliance number in trees
zbMATH Open document ID: 1230.05224
author: Xuegang Chen
author: Wai Chee Shiu
published in: The Electronic Journal of Combinatorics
publication date: 2011-10-18T00:00:00Z
full work available at URL: v18i1p202.html
review text: Summary: A global defensive alliance in a graph \(G = (V, E)\) is a dominating set \(S\) satisfying the condition that for every vertex \(v \in S\), \(|N [v] \cap S| \geq |N (v) \cap (V - S)|\). In this note, a new upper bound on the global defensive alliance number of a tree is given in terms of its order and the number of support vertices. Moreover, we characterize trees attaining this upper bound.
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 5960064
zbMATH Keywords: global defensive alliance number
zbMATH Keywords: tree
zbMATH Keywords: upper bound
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5960064