Adiabatic Quantum Computation (AQC) is a model of computation equivalent to standard quantum computation and based on the adiabatic theorem of Quantum Mechanics. The idea behind AQC is to prepare the system in the ground state of a simple Hamiltonian and let the system adiabatically evolve to a Hamiltonian whose ground state encodes the solution to the problem of interest. In this talk I will discuss a quantum algorithm for the Graph Isomorphism problem based on AQC. In particular, I will focus on how a careful choice of the initial Hamiltonian can probably reduce the complexity of the problem.