Isomorphisms Involving Reversing Arcs of Digraphs

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.