In this paper the use of graph isomorphism is investigated within the framework of symmetry breaking in constraint satisfaction problems. A running example of Comma-free codes is used to test the methods. But the technique can be extended to other problems. In particular Symmetry Breaking via Dominance Detection (SBDD) is applied to find Comma-Free Codes. To check if a current partial solution is symmetrically equivalent to a previously found no-good, graph isomorphism is used. In particular the powerful and fast graph isomorphism package nauty is used. Experimental results show that for