On the cardinality of a factor set of binary matrices

The work considers an equivalence relation in the set of all n×m binary matrices. In each element of the factor-set generated by this relation, we define the concept of canonical binary matrix, namely the minimal element with respect to the lexicographic order. For this purpose, the binary matrices are uniquely represented by ordered n-tuples of integers. We have found a necessary and sufficient condition for an arbitrary matrix to be canonical. This condition could be the base for realizing recursive algorithm for finding all n×m canonical binary matrices and consequently for finding all bipartite graphs, up to isomorphism with cardinality of each part equal to n and m.