Opuscula Math. 24, no. 2 (2004), 189-196
NP-completeness of weakly convex and convex dominating set decision problems
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.