There is a unique group, called the fundamental group, canonically associated to each finite connected graph of groups.

The question of reconstructibility for locally finite infinite graphs is still open.

Theoretical analytical results exploit and further develop some fundamental properties of random walks in finite graph.

Solving a parity game played on a finite graph means deciding, for a given starting position, which of the two players has a winning strategy.

Another influential paper of Stalling is his 1983 article "Topology on finite graphs".

Let G be a finite connected graph.

Thus the class of all finite graphs is not an elementary class (the same holds for many other algebraic structures).

They show that, when G is a finite connected graph, only four possible behaviors are possible for this sequence:

However, there are no finite t-transitive graphs of degree 3 or more for t 8.

Each solution involves looking a labyrinth as a finite connected graph, where the width of the graph does not matter.