Therefore, we only need to consider the sum of all connected graphs without subtadpoles.

Any connected graph without simple cycles is a tree.

That is, a 1-tree is a connected graph containing exactly one cycle.

A strong orientation is an orientation that results in a strongly connected graph.

A tree is a connected graph with no cycles.

But only a connected graph has a spanning tree.

In other words, any connected graph without simple cycles is a tree.

In the other direction, it is necessary to show that every connected bridgeless graph can be strongly oriented.

There is also a criterion for regular and connected graphs :

Afterwards, paths are established connecting these links, to create a connected graph.