Geodesic
On twin edge colorings of graphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 613-627

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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
Keywords: edge coloring, vertex coloring, factorization 
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Andrews, Eric; Helenius, Laars; Johnston, Daniel; VerWys, Jonathon; Zhang, Ping. On twin edge colorings of graphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 613-627. http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a13/