A New Upper Bound on the Global Defensive Alliance Number in Trees

Xue-gang Chen; Wai Chee Shiu

doi:10.37236/689

A New Upper Bound on the Global Defensive Alliance Number in Trees

Xue-gang Chen
, Wai Chee Shiu

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

2 Citations (Scopus)

Abstract

A global defensive alliance in a graph G = (V,E) is a dominating set S satisfying the condition that for every vertex v ∈ S, |N[v] ∩ S| ≥ |N(v) ∩ (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.

Original language	English
Article number	P202
Number of pages	7
Journal	Electronic Journal of Combinatorics
Volume	18
Issue number	1
DOIs	https://doi.org/10.37236/689
Publication status	Published - 10 Oct 2011

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Global defensive alliance number
Tree
Upper bound

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abstract = "A global defensive alliance in a graph G = (V,E) is a dominating set S satisfying the condition that for every vertex v ∈ S, |N[v] ∩ S| ≥ |N(v) ∩ (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.",

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A New Upper Bound on the Global Defensive Alliance Number in Trees

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