Introduction to dominated edge chromatic number of a graph

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