2013/07/19 by Alexandria Yu, Yu, Alexandria
Mathematics · #97Kxx #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:97Kxx
paper · pdf · doi:10.48550/arxiv.1307.5808
arxiv created 2013/07/19 · arxiv updated 2013/07/23
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 S is chosen, at least half of the points in its neighborhood are also in the set S, including the selected point. A global offensive alliance is a dominating set such that if any point outside S is selected, at least half of the points in its neighborhood, including the selected point, are in set S. Our result answers an open question in [HA].