TWIN EDGE COLORING OF SOME PATH AND CYCLE RELATED GRAPHS

A twin edge -coloring of a graph is a proper edge -coloring of with the elements of so that the induced vertex -coloring, in which the color of a vertex in is the sum in of the colors of the edges incident with is a proper vertex - coloring. The minimum for which has a twin edge k- coloring is called the twin chromatic index of . Twin chromatic index of the splitting graph of path and cycle, middle graph of path and cycle and shadow graph of path and cycle are determined. Twin chromatic index of is also determined, where denotes the direct product of and are, respectively, the cycle and the path on r vertices each.