Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Antoni Benseny i Nacho López[en] This project has got two main objectives. The first one is to give a general idea of the degree/diameter problem, especially for mixed proper graphs, to be useful as a simple but complete introduction to whomever wants to work on it. The second goal is to solve, or at least make an improvement, on two particular cases for proper mixed Cayley abelian graphs.