Introduction to dominated edge chromatic number of a graph

• Main Authors: Piri, Mohammad R, Alikhani, Saeid
• Format: Journal Article
• Language: English
• Published: 19.03.2020
• Subjects: Mathematics - Combinatorics
• DOI: 10.48550/arxiv.2003.10232

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 we 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.