# Article

Full entry | PDF   (0.9 MB)
Keywords:
dominating set; point-set dominating set; point-set domatic number; bipartite graph
Summary:
A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called point-set dominating, if for each subset $S\subseteq V(G)-D$ there exists a vertex $v\in D$ such that the subgraph of $G$ induced by $S\cup\{v\}$ is connected. The maximum number of classes of a partition of $V(G)$, all of whose classes are point-set dominating sets, is the point-set domatic number $d_p(G)$ of $G$. Its basic properties are studied in the paper.
References:
[1] Cockayne E. J., Hedetniemi S. T.: Towards the theory of domination in graphs. Networks 7 (1977), 247-261. DOI 10.1002/net.3230070305 | MR 0483788
[2] Haynes T. W., Hedetniemi S. T., Slater P. J.: Fundamentals of Domination in Graphs. Marcel Dekker, Inc., New York, 1998. MR 1605684 | Zbl 0890.05002
[3] Pushpa Latha L.: The global point-set domination number of a graph. Indian J. Pure Appl. Math. 28 (1997), 47-51, MR 1442817 | Zbl 0871.05036
[4] Sampathkumar E., Pushpa Latha L.: Point-set domination number of a graph. Indian J. Pure Appl. Math. 24 (1993), 225-229. MR 1218532 | Zbl 0772.05055
[5] Sampathkumar E., Pushpa Latha L.: Set domination in graphs. J. Graph Theory 18 (1994), 489-495. DOI 10.1002/jgt.3190180507 | MR 1283314 | Zbl 0807.05066

Partner of