On k-dependent domination

Authors:
O. Favaron;S. M. Hedetniemi;S. T. Hedetniemi;D. F. Rall
Affiliations:
Université de Paris-Sud Orsay Cedex, France;Department of Computer Science, Clemson University, Edwards Hall, Box-341906 Clemson, SC;Department of Computer Science, Clemson University, Edwards Hall, Box-341906 Clemson, SC;Furman University Greenville, SC
Venue:
Discrete Mathematics
Year:
2002

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Abstract

A k-dependent dominating set D in a graph G = (V,E) is a set which is both k-dependent and dominating, where a set is k-dependent if the maximum degree of a vertex in the subgraph 〈D〉 induced by D is at most k, and a set D is dominating if every vertex not in D is adjacent to at least one vertex in D. This paper introduces the concept of k-dependent domination and establishes close relationships between k-dependent domination and the standard concepts of domination and irredundance in graphs. Computational complexity questions corresponding to the decision problems associated with k-dependent dominating sets and k-dependent irredundant sets are also answered.