University of Twente, Department of Applied Mathematics
Abstract
The concept of a line digraph is generalized to that of a directed path graph. The directed path graph Pk(D) of a digraph D is obtained by representing the directed paths on k vertices of D by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in D form a directed path on k + 1 vertices or form a directed cycle on k vertices in D. Several properties of Pk(D) are studied, in particular with respect to isomorphism and traversability