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Independent set dominanting sets in bipartite graphs

Zelinka B.

Opuscula Mathematica

2005

Vol. 25, no. 2

345-349

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 ikkeq V(G) - D there exists a set Y ikkeq D such that the subgraph of G induced X cup Y is connected. The minimum number of vertices of an sd-set in G is called the set domination number gammas (G) of G. An sd-set D in G such that /D/ = gammas(G) is called a gammas-set in G. In this paper we study sd-sets in bipartite graphs which are simultaneously independent. We apply the theory of hypergraphs.