A twin edge k-coloring of a graph G is a proper edge coloring of G with the elements of Z_(k) so that the induced vertex coloring in which the color of a vertex v in G is the sum (in Z_(k)) of the colors of the edges incident with v is a proper vertex coloring. The minimum k for which G has a twin edge k-coloring is called the twin chromatic index of G. Among the results presented are formulas for the twin chromatic index of each complete graph and each complete bipartite graph.
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