ON TWIN EDGE COLORING OF SOME LADDER GRAPHS, LINE GRAPH OF COMB GRAPH AND TWIG GRAPH

A twin k-edge coloring of a graph G is a proper edge coloring of G that requires colors from Z k and that induced a proper vertex coloring on G, where the color of a vertex v is the sum in Z k of the colors of the edges incident with v. The least k for which G has a twin edge k-coloring is known as twin chromatic index of G and it is denoted by χt′(G). In this paper, we obtained the twin chromatic index of ladder graph, triangular ladder graph, slanting ladder graph, line graph of comb graph and line graph of twig graph.