A Sufficient Condition for Oriented Graphs to be Hamiltonian

Abstract

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