Brushing directed graphs

Abstract

Brushing of graphs is an edge searching strategy where the searching agents are called brushes. We focus on brushing directed graphs based on a new model that we have developed. The fundamentals of this model have been influenced by previous studies about brushing undirected graphs. We discuss strategies to brush directed graphs as well as values and bounds for the brushing number of directed graphs. As the main results we give an upper bound for the brushing number of directed acyclic graphs. We also establish exact values for the brushing number of transitive tournaments, complete directed graphs and rotational tournaments. The behaviour of the brushing number of several other types of directed graphs are also taken into consideration.