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

Abstract

A twin edge K-coloring of a graph  is a proper edge K-coloring  of G with the elements of Z_k so that the induced vertexK-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 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 C_m X P_n is also determined, where Xdenotes the direct product of C_r and P_r are, respectively, the cycle and the path on r vertices each.