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

Authors:
Mustapha Chellali;Odile Favaron;Adriana Hansberg;Lutz Volkmann
Affiliations:
University of Blida, LAMDA-RO Laboratory, Department of Mathematics, B.P. 270, Blida, Algeria;LRI, URM 8623, University Paris-Sud and CNRS, 91405, Orsay Cedex, France;Edifici C2, UPC Barcelona, Dep. Matemàtica Aplicada III, C/ Jordi Girona 1 i 3, 08034, Barcelona, Spain;RWTH Aachen University, Lehrstuhl II für Mathematik, Templergraben 55, 52056, Aachen, Germany
Venue:
Graphs and Combinatorics
Year:
2012

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Abstract

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.