An inequality on global alliances for trees
Combinatorics
2013-07-23 v1
Abstract
In this paper, we prove an inequality on the cardinalities of the minimum size global defensive alliance and the minimum size global offensive alliance. A global defensive alliance is a dominating set such that when any point inside a selected group is chosen, at least half of the points in its neighborhood are also in the set , including the selected point. A global offensive alliance is a dominating set such that if any point outside is selected, at least half of the points in its neighborhood, including the selected point, are in set . Our result answers an open question in [HA].
Cite
@article{arxiv.1307.5808,
title = {An inequality on global alliances for trees},
author = {Alexandria Yu},
journal= {arXiv preprint arXiv:1307.5808},
year = {2013}
}