A graph matching algorithm is illustrated and its performance compared with that of a well known algorithm performing the same task. According to the proposed algorithm, the matching process is carried out by using a State Space Representation: a state represents a partial solution of the matching between two graphs, and a transition between states corresponds to the addition of a new pair of matched nodes. A set of feasibility rules is introduced for pruning states corresponding to partial matching solutions not satisfying the required graph morphism. Results outlining the computational cost reduction achieved by the method are given with reference to a set of randomly generated graphs.