Orientable Graphs

# Orientable Graphs

Definition: A digraph $D$ is said to be Orientable if there exists an orientation (a selection of arc directions) that makes $D$ strongly connected (there exists a directed path between each pair of vertices). |

Definition: An Orientation of a graph $G$ is the replacement of all edges $\{ x, y \} \in E(G)$ with either the arc $(x, y)$ or $(y, x)$. |

A good example of an orientable graph is the following digraph $D$:

When we reorient the edges, we can easily get a strongly connected digraph:

Hence, the original digraph $D$ is orientable.