The topological ordering of covering nodes

Abstract

The topological ordering algorithm sorts nodes of a directed graph such that the order of the tail of each arc is lower than the order of its head. In this paper, we introduce the notion of covering between nodes of a directed graph. Then, we apply the topological ordering algorithm on graphs containing the covering nodes. We show that there exists a cut set with forward arcs in these graphs and the order of the covering nodes is successive.

Keywords

• directed graph
• covering nodes
• topological ordering algorithm