On F-domination in graphs

Abstract Let G = ( V , E ) be a graph and let F be a family of subsets of V such that ⋃ F ∈ F F = V . A dominating set D of G is called an F -dominating set if D ∩ F ≠ ∅ for all F ∈ F . The minimum cardinality of an F -dominating of G is called the F -domination number of G and is denoted by γ F ( G ) . In this paper we present several basic results on this parameter. We also introduce the concept of F -irredundance and obtain an inequality chain four parameters.