IJPAM: Volume 43, No. 1 (2008)


Dorota Bród
Faculty of Mathematics and Applied Physics
Technical University of Rzeszów
2, ul. W. Pola, Rzeszów, 35-959, POLAND
e-mail: dorotab@prz.edu.pl

Abstract.A subset $S\subseteq V(G)$ is a weak dominating set of a graph $G$ if for any vertex $y\in V(G)-S$ there exists a vertex $x\in S$ adjacent to $y$ and such that $\text{\rm deg}\,_G\,(x)\le \text{\rm deg}\,_G\,(y)$. A minimal weak dominating set $S$ of $G$ is a weak dominating set that contains no weak dominating set of $G$ as a proper subset. The total number of the mentioned dominating sets for some classes of graphs is determined.

Received: December 18, 2007

AMS Subject Classification: 05C20

Key Words and Phrases: weak dominating set, minimal weak dominating set

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 43
Issue: 1