INTRODUCTION TO DOMINATED EDGE CHROMATIC NUMBER OF A GRAPH

We introduce and study the dominated edge coloring of a graph. A dominated edge coloring of a graph G, is a proper edge coloring of G such that each color class is dominated by at least one edge of G. The minimum number of colors among all dominated edge coloring is called the dominated edge chromatic number, denoted by chi'(dom)(G). We obtain some properties of chi'(dom)(G) and compute it for specific graphs. Also examine the effects on chi'(dom)(G), when G is modified by operations on vertex and edge of G. Finally, we consider the k-subdivision of G and study the dominated edge chromatic number of these kind of graphs.