Generalized perfect domination in graphs

Authors:
B. Chaluvaraju;K. A. Vidya
Affiliations:
Department of Mathematics, Bangalore University, Bangalore, India 560 001;Department of Mathematics, Bangalore University, Bangalore, India 560 001
Venue:
Journal of Combinatorial Optimization
Year:
2014

Citing 3
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Abstract

Let k be a positive integer and G=(V,E) be a graph. A vertex subset D of a graph G is called a perfect k-dominating set of G, if every vertex v of G, not in D, is adjacent to exactly k vertices of D. The minimum cardinality of a perfect k-dominating set of G is the perfect k-domination number 驴 kp (G). In this paper, we give characterizations of graphs for which 驴 kp (G)=驴(G)+k驴2 and prove that the perfect k-domination problem is NP-complete even when restricted to bipartite graphs and chordal graphs. Also, by using dynamic programming techniques, we obtain an algorithm to determine the perfect k-domination number of trees.