TY  - JOUR
ID  - Zelinka2005
LB  - Zelinka2005
AU  - Zelinka, Bohdan
TI  - Independent set dominating sets in bipartite graphs
ST  - Independent set dominating sets in bipartite graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2005
VL  - 25
IS  - 2
SP  - 345
EP  - 349
DO  - http://dx.doi.org/10.7494/OpMath.2005.25.2.345
UR  - http://dx.doi.org/10.7494/OpMath.2005.25.2.345
AB  - 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.
KW  - set dominating set
KW  - set domination number
KW  - independent set
KW  - bipartite graph
KW  - multihypergraph
SN  - 1232-9274
ER  -