Abstract#R##N##R##N#Let f be an integer valued function defined on the vertex set V(G) of a simple graph G. We call a subset Df of V(G) a f-dominating set of G if |N(x, G) ∩ Df| ≥ f(x) for all x ∈ V(G) — Df, where N(x, G) is the set of neighbors of x.Df is a minimum f-dominating set if G has no f-dominating set D′f with |Df| < |Df|. If j, k ∈ N0 = {0,1,2,…} with j ≤ k, then we define the integer valued function fj,k on V(G) by #R##N##R##N##R##N##R##N##R##N##R##N##R##N#.#R##N##R##N##R##N##R##N#By μj,k(G) we denote the cardinality of a minimum fj,k-dominating set of G.#R##N##R##N##R##N##R##N#A set D ⊆ V(G) is j-dominating if every vertex, which is not in D, is adjacent to at least j vertices of D. The j-domination number γj(G) is the minimum order of a j-dominating set in G.#R##N##R##N##R##N##R##N#In this paper we shall give estimations of the new domination number μj,k(G), and with the help of these estimations we prove some new and some known upper bounds for the j-domination number. © 1993 John Wiley & Sons, Inc.
['Christoph Stracke', 'Lutz Volkmann']
A new domination conception