Opuscula Math. 25, no. 2 (2005), 345-349

 
Opuscula Mathematica

Independent set dominating sets in bipartite graphs

Bohdan Zelinka

Abstract. The paper continues the study of independent set dominating sets in graphs which was started by E. Sampathkumar. A subset \(D\) of the vertex set \(V(G)\) of a graph \(G\) is called a set dominating set (shortly sd-set) in \(G\), if for each set \(X \subseteq V(G)-D\) there exists a set \(Y \subseteq D\) such that the subgraph \(\langle X \cup Y\rangle\) of \(G\) induced by \(X \cup Y\) is connected. The minimum number of vertices of an sd-set in \(G\) is called the set domination number \(\gamma_s(G)\) of \(G\). An sd-set \(D\) in \(G\) such that \(|D|=\gamma_s(G)\) is called a \(\gamma_s\)-set in \(G\). In this paper we study sd-sets in bipartite graphs which are simultaneously independent. We apply the theory of hypergraphs.

Keywords: set dominating set, set domination number, independent set, bipartite graph, multihypergraph.

Mathematics Subject Classification: 05C69, 05C65.

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Bohdan Zelinka, Independent set dominating sets in bipartite graphs, Opuscula Math. 25, no. 2 (2005), 345-349

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