MATHEMATICA BOHEMICA, Vol. 124, No. 1, pp. 77-82 (1999)

Point-set domatic numbers of graphs

Bohdan Zelinka

Bohdan Zelinka, Katedra aplikované matematiky Technické univerzity, Voronezska 13, 461 17 Liberec 1, Czech Republic

Abstract: 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.

Keywords: dominating set, point-set dominating set, point-set domatic number, bipartite graph

Classification (MSC2000): 05C35

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number]
© 2004—2005 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition