Twin edge colorings of certain square graphs and product graphs - R Rajarajachozhan; R. Sampathkumar (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2016)
A twin edge k\!-coloring of a graph G is a proper edge k-coloring of G with the elements of Z_k so that the induced vertex k-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 k\!-coloring. The minimum k for which G has a twin edge k\!-coloring is called the twin chromatic index of G. Twin chromatic index of the square P_n^2, n4, and the square C_n^2, n6, are determined. In fact, the twin chromatic index of the square C_7^2 is Δ+2, where Δ is the maximum degree. Twin chromatic index of C_m P_n is determined, where denotes the Cartesian product. C_r and P_r are, respectively, the cycle, and the path on r vertices each.