Independent set dominating sets in bipartite graphs
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 \subsete...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AGH Univeristy of Science and Technology Press
2005-01-01
|
| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol25/2/art/opuscula_math_2525.pdf |
| Summary: | 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. |
|---|---|
| ISSN: | 1232-9274 |