The Isomorphism Problem For Directed Path Graphs and For Rooted Directed Path Graphs

This paper deals with the isomorphism problem of directed path graphs and rooted directed path graphs. Both graph classes belong to the class of chordal graphs, and for both classes the relative complexity of the isomorphism problem is yet unknown. We prove that deciding isomorphism of directed path graphs is isomorphism complete, whereas for rooted directed path graphs we present a polynomial-time isomorphism algorithm.