Oriented bipartite graphs and the Goldbach graph

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-known Caccetta-Häggkvist Conjecture graphs some cases which it is unsolved, general, also concept undirected as well “odd-even” terms them. fact, any graph (acyclic graph) can be represented by odd-even (oriented graph). obtain conditions connectedness This their motivated special family call “Goldbach graphs”. famous Goldbach's conjecture Goldbach other theoretic conjectures (e.g., twin prime conjecture) related various parameters graphs, motivating us nature vertex-degrees independent sets these Finally, observe properties small vertices.