POWER DOMINATOR EDGE COLORING OF LINE GRAPH AND DEGREE SPLITTING OF SOME CERTAIN CLASSES OF GRAPHS

Abstract

A dominator edge coloring of ????, is a proper edge coloring of ????, in which every edge of some color class (possibly its own class) are dominated by every edge in ????. The dominator edge chromatic number of ???? is the minimum number of distinct color classes required in a dominator edge coloring of ????, denoted by????????′ (????). We introduced the variate known as power dominator edge coloring based on the notion of power edge domination and determine the power dominator edge chromatic number for certain classes of graph. Power Dominator Edge Coloring of a graph G, refers to the proper edge coloring where each edge in the edge set power dominates every edge of at least one-color class. The Power Dominator Edge Chromatic number (PDEC-number)????????????′(????), is the minimum number of colors that a power dominator edge coloring of the graph requires [6]. Here we determine the PDEC-number for the line graph and for degree splitting of some certain classes of graphs.