New upper bound on the global defensive alliance number in trees

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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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Chen, X. G., & Shiu, W. C. (2011). New upper bound on the global defensive alliance number in trees. Electronic Journal of Combinatorics, 18(1), 1–7. https://doi.org/10.37236/689

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