Generalized independence and domination in graphs

AbstractThe purpose of this paper is to introduce various concepts of P-domination, which generalize and unify different well-known kinds of domination in graphs. We generalize a result of Lovász concerning the existence of a partition of a set of vertices of G into independent subsets and a result of Favaron concerning a property of Sk-dominating sets. Gallai-type equalities for the strong P-domination number are proved, which generalize Nieminen's result