Opuscula Math. 24, no. 2 (2004), 189-196

Opuscula Mathematica

# NP-completeness of weakly convex and convex dominating set decision problems

Joanna Raczek

Abstract. The convex domination number and the weakly convex domination number are new domination parameters. In this paper we show that the decision problems of convex and weakly convex dominating sets are $$NP$$-complete for bipartite and split graphs. Using a modified version of Warshall algorithm we can verify in polynomial time whether a given subset of vertices of a graph is convex or weakly convex.

Keywords: dominating set, $$NP$$-completeness, distance, convex set.

Mathematics Subject Classification: 05C69, 05C85.

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• Joanna Raczek
• Gdańsk University of Technology, Department of Mathematics, ul. Narutowicza 11/12, 80-952 Gdańsk, Poland