k-Domination and k-Independence in Graphs: A Survey.

In 1985, Fink and Jacobson gave a generalization of the concepts of domination and independence in graphs. For a positive integer k, a subset S of vertices in a graph G = ( V, E) is k- dominating if every vertex of V − S is adjacent to at least k vertices in S. The subset S is k- independent if the maximum degree of the subgraph induced by the vertices of S is less or equal to k − 1. In this paper we survey results on k-domination and k-independence. [ABSTRACT FROM AUTHOR]