Isomorphisms Involving Reversing Arcs of Digraphs

Abstract

A digraph $D$ is reversible if it is isomorphic to the digraph obtained by reversing all arcs of $D$. A digraph is subreversible if adding any arc between two non-adjacent vertices results in a reversible digraph. We characterize all subreversible digraphs which do not contain cycles of length 3 or 4.