Article ID Journal Published Year Pages File Type
421216 Discrete Applied Mathematics 2012 11 Pages PDF
Abstract

A directed dominating set in a directed graph DD is a set SS of vertices of VV such that every vertex u∈V(D)∖Su∈V(D)∖S has an adjacent vertex vv in SS with vv directed to uu. The directed domination number of DD, denoted by γ(D)γ(D), is the minimum cardinality of a directed dominating set in DD. The directed domination number of a graph GG, denoted by Γd(G)Γd(G), is the maximum directed domination number γ(D)γ(D) over all orientations DD of GG. The directed domination number of a complete graph was first studied by Erdös [P. Erdös, On Schütte problem, Math. Gaz. 47 (1963) 220–222], albeit in disguised form. The authors [Y. Caro, M.A. Henning, A Greedy partition lemma for directed domination, Discrete Optim. 8 (2011) 452–458] recently extended this notion to directed domination of all graphs. In this paper we continue this study of directed domination in graphs. We show that the directed domination number of a bipartite graph is precisely its independence number. Several lower and upper bounds on the directed domination number are presented.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
Authors
, ,