Eulerian iterated line graphs and digraphs Original Research Article

It is shown that every strongly connected digraph has either at most one or infinitely many of its iterated line digraphs eulerian. The proof uses a canonical way of ‘wrapping’ a digraph D around a directed cycle whose length is the greatest common divisor of all directed-cycle lengths of D. A simple characterization of undirected graphs with some iterated line graph eulerian is also given.