Integer and fractional security in graphs

Let G = (V,E) be a graph. A subset S of V is said to be secure if it can defend itself from an attack by vertices in N [S]− S. In the usual definition, each vertex in N [S]− S can attack exactly one vertex in S, and each vertex in S can defend itself or one of its neighbors in S. A defense of S is successful if each vertex has as many defenders as attackers… (More)