On edge transitivity of directed graphs Original Research Article

We examine edge transitivity of directed graphs. The class of local comparability graphs is defined as the underlying graphs of locally edge transitive digraphs. The latter generalize edge transitive orientations, while local comparability graphs include comparability, anticomparability, and circle graphs. Recognizing local comparability graphs is NP-complete, however, they are differences of comparability graphs. The concept of dimension is defined so as to generalize that of an edge transitive digraph. Connected proper interval graphs are characterized as exactly the class of local comparability graphs of dimension one. Finally, a new characterization of circle graphs is given also in terms of edge transitivity.