Robbins' theorem states that an undirected graph has a graph orientation that is a strongly connected digraph iff it is a connected graph with no graph bridges (Robbins 1939). This guarantees that the oriented diameter is defined for every such graph.
Robbins' Theorem
See also
Graph Bridge, Graph Orientation, Oriented Diameter, Strongly Connected DigraphExplore with Wolfram|Alpha
References
Robbins, H. E. "A Theorem on Graphs with an Application to a Problem of Traffic Control." Amer. Math. Monthly 46, 281-283, 1939.Cite this as:
Weisstein, Eric W. "Robbins' Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RobbinsTheorem.html