An \((n+1)\)-edge-colored graph is said to be \(m\)-bipartite if \(m\) is the largest integer so that every connected subgraph whose edges are colored by only \(m\) colors is bipartite. The authors assign a numerical code of length \((2n- m+1)\times q\) to each \(m\)-bipartite \((n+1)\)-edge-colored graph of order \(2q\). They prove that two such graphs have the same code if and only if a graph isomorphism exists which transforms the graphs into each other, up to permutation of the edge-coloring.