This thesis would like to extend some concepts of an existing representation theory for closed PL manifolds, called Crystallization Theory. This theory has the peculiarity of using a particular class of regular edge-coloured (multi)graphs (called crystallizations) to represent PL manifolds, so that topological properties can be translated into combinatorial ones (PL invariants of manifolds can be computed directly on the representing graphs).

Firstly, we introduce concepts on Combinatorial Topology and on Graph Theory in order to construct such particular graphs. Then, properties, classic results and the computation of an important topological invariant (Fundamental Group) will be mentioned.

In the main part of the work we study a local operation on a graph, called switching of a \rho-pair, which allows to minimize a graph without changing the underlying PL structure and generalize its property to graphs representing general polyhedra (a sketch of the proof is given).

Then, we focus on the 3-dimensional case. After some basic definitions, we prove that the relations between Heegaard splittings or diagrams and edge-coloured graphs still hold for manifolds with non-empty boundary and that the classical topological invariant, the Heegaard genus, and the totally combinatorial invariant, the regular genus, coincide for all compact 3-manifolds (again a sketch of the proof is described).

Finally, we study the connections between planarity of graphs and regular planar embeddings of edge-coloured graphs: we establish a little result concerning non-planarity of simple graphs that allows to exclude planar simple graphs as representatives of PL n-manifolds, with n\ge 3.