A digraph equation for homomorphic images (Q1084405)

A homomorphism \(\phi\) (respectively contraction \(\theta)\) of a graph G is a sequence of identifications of two non-adjacent (respectively adjacent) vertices of G. The authors extend these definitions to digraphs. They prove that \(\overline{\phi (D)}=\theta_{\phi}(\bar D)\) for all homomorphisms \(\phi\) of D if and only if D is pseudo-complete-n-partite.