Global defensive alliances in graphs
The electronic journal of combinatorics, Tome 10 (2003)
A defensive alliance in a graph $G = (V,E)$ is a set of vertices $S \subseteq V$ satisfying the condition that for every vertex $v \in S$, the number of neighbors $v$ has in $S$ plus one (counting $v$) is at least as large as the number of neighbors it has in $V-S$. Because of such an alliance, the vertices in $S$, agreeing to mutually support each other, have the strength of numbers to be able to defend themselves from the vertices in $V-S$. A defensive alliance $S$ is called global if it effects every vertex in $V-S$, that is, every vertex in $V-S$ is adjacent to at least one member of the alliance $S$. Note that a global defensive alliance is a dominating set. We study global defensive alliances in graphs.
@article{10_37236_1740,
author = {Teresa W. Haynes and Stephen T. Hedetniemi and Michael A. Henning},
title = {Global defensive alliances in graphs},
journal = {The electronic journal of combinatorics},
year = {2003},
volume = {10},
doi = {10.37236/1740},
zbl = {1031.05096},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1740/}
}
Teresa W. Haynes; Stephen T. Hedetniemi; Michael A. Henning. Global defensive alliances in graphs. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1740
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