Geodesic
A new upper bound on the global defensive alliance number in trees
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/689
Classification : 05C69, 05C05, 05C35
Mots-clés : global defensive alliance number, tree, upper bound 
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     author = {Xue-gang Chen and Wai Chee Shiu},
     title = {A new upper bound on the global defensive alliance number in trees},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/689},
     zbl = {1230.05224},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/689/}
}
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Xue-gang Chen; Wai Chee Shiu. A new upper bound on the global defensive alliance number in trees. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/689

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