Introduction to dominated edge chromatic number of a graph

• Published in: Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica Vol. 41; no. 2; pp. 245 - 257
• Main Authors: Piri, Mohammad R., Alikhani, Saeid
• Format: Journal Article
• Language: English
• Published: AGH Univeristy of Science and Technology Press 01.01.2021
• Subjects: corona; dominated edge chromatic number; operation; subdivision
• ISSN: 1232-9274
• DOI: 10.7494/OpMath.2021.41.2.245

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 \(\chi_{dom}^{\prime}(G)\). We obtain some properties of \(\chi_{dom}^{\prime}(G)\) and compute it for specific graphs. Also examine the effects on \(\chi_{dom}^{\prime}(G)\), 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.