A Sufficient Condition for Oriented Graphs to be Hamiltonian

In this paper, we prove the following result:
Let \(D\) be a disconnected oriented graph of order \(n\). If
\(d^+(u)+d^+(v) \geq n-2\) for any pair \(u,v\) of nonadjacent vertices such that \(N^+(u) \cap N^+(v) \neq \emptyset\) and \(d^-(u) + d^-(v) \geq n-2\) for any pair \(u,v\) of nonadjacent vertices such that \(N^-(u) \cap N^-(v) \neq \emptyset\), then \(D\) contains a directed Hamiltonian cycle.