(F,I)-security in graphs

Let G=(V,E) be a graph and S⊆V. A set S is (F,I)-secure if every (possibly fractional) attack can be defended by an integer defense. A necessary and sufficient condition for S to be (F,I)-secure is given. For a graph G, the (F,I)-security number of G is the cardinality of a smallest (F,I)-secure set of G. The (F,I)-security number for various classes of graphs is determined. It is also shown that ultra-security implies (F,I)-security. Some partial results and areas for further study are included.