A cancellation graph G is one for which given any graph C, we have G\times C\cong X\times C implies G\cong X. In this thesis, we characterize all bipartite cancellation graphs. In addition, we characterize all solutions X to G\times C\cong X\times C for bipartite G. A characterization of non-bipartite cancellation graphs is yet to be found. We present some examples of solutions X to G\times C\cong X\times C for non-bipartite G, an example of a non-bipartite cancellation graph, and a conjecture regarding non-bipartite cancellation graphs.