In this paper, we study oriented bipartite graphs. particular, introduce “bitransitive” Several characterizations of bitransitive bitournaments are obtained. We show that bitounaments equivalent to acyclic bitournaments. As applications, characterize with Hamiltonian paths, determine the number non-isomorphic a given order, and solve graph-isomorphism problem in linear time for Next, prove well...

An oriented graph is a digraph with no opposite arcs. The oriented chromatic number of an oriented graph G⃗ is the minimum order of an oriented graph to which G⃗ admits a homomorphism. The oriented chromatic number of an undirected graph is then defined as the maximum oriented chromatic number of its orientations. In this paper, we survey the main results about this graph parameter and propose a ...

‎an  oriented perfect path double cover (oppdc) of a‎ ‎graph $g$ is a collection of directed paths in the symmetric‎ ‎orientation $g_s$ of‎ ‎$g$ such that‎ ‎each arc‎ ‎of $g_s$ lies in exactly one of the paths and each‎ ‎vertex of $g$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎maxov{'a} and ne{v{s}}et{v{r}}il (discrete‎ ‎math‎. ‎276 (2004) 287-294) conjectured that ...

Oriented graphs are directed graphs without opposite arcs. In other words an oriented graph is an orientation of an undirected graph, obtained by assigning to every edge one of the two possible orientations. IfG is a graph, V (G) denotes its vertex set, E(G) denotes its set of edges (or arcs if G is an oriented graph) and F (G) denotes its set of faces if G is planar. A homomorphism from an ori...