Decomposition and enumeration of triangulated surfaces

We describe some theoretical results on triangulations of surfaces and we develop a theory on roots, decompositions, and genus surfaces. We apply this theory to describe an algorithm to list all triangulations of closed surfaces with at most a fixed number of vertices. We specialize the theory to the case that the number of vertices is at most 11, and we obtain theoretical restrictions on genus surfaces, allowing us to obtain a list of all triangulations of closed surfaces with at most 11 vertices.