Global alliances and independence in trees

Mustapha Chellali, Teresa W. Haynes
2007 Discussiones Mathematicae Graph Theory  
A global defensive (respectively, offensive) alliance in a graph G = (V, E) is a set of vertices S ⊆ V with the properties that every vertex in V − S has at least one neighbor in S, and for each vertex v in S (respectively, in V − S) at least half the vertices from the closed neighborhood of v are in S. These alliances are called strong if a strict majority of vertices from the closed neighborhood of v must be in S. For each kind of alliance, the associated parameter is the minimum cardinality
more » ... inimum cardinality of such an alliance. We determine relationships among these four parameters and the vertex independence number for trees.
doi:10.7151/dmgt.1340 fatcat:l4mze3qe2vb27hef4qkojpawyi