A twin edge k-coloring of a graph G is a proper edge coloring of G with the elements of Zk so that the induced vertex coloring in which the color of a vertex v in G is the sum (in Zk) 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
@article{bwmeta1.element.doi-10_7151_dmgt_1756, author = {Eric Andrews and Laars Helenius and Daniel Johnston and Jonathon VerWys and Ping Zhang}, title = {On Twin Edge Colorings of Graphs}, journal = {Discussiones Mathematicae Graph Theory}, volume = {34}, year = {2014}, pages = {613-627}, zbl = {1305.05068}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1756} }
Eric Andrews; Laars Helenius; Daniel Johnston; Jonathon VerWys; Ping Zhang. On Twin Edge Colorings of Graphs. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 613-627. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1756/
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