Twin Edge Coloring of Some Path and Cycle Related Graphs: A Recent Study

A twin edge K-coloring of a graph is a proper edge K-coloring of G with the elements of Zk so that the induced vertexK-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 vertexK-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 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 Cm X Pn is also determined, where Xdenotes the direct product of Cr and Pr are, respectively, the cycle and the path on r vertices each.