Is there - say, for a triangulable surface - a concrete algorithm how to calculate the fundamental group of the surface from a given triangulation, seen as a graph (of its 1-skeleton), given as an adjacency matrix?
If there is such an algorithm: Does every triangulation do the job (as an input of the algorithm)?
(Specifically: Which (serious) algorithm gives back the trivial group for input $K_4$ and $\mathbb{Z} \times \mathbb{Z}$ for input $K_7$?)
Or is this kind of question just too naive?