论文标题
统治的边缘色度介绍图的图
Introduction to dominated edge chromatic number of a graph
论文作者
论文摘要
我们介绍并研究图的主导边缘着色。图$ g $的主导边缘着色是$ g $的适当边缘着色，因此每个颜色类别至少由$ g $的一个边缘主导。所有主导边缘着色中的最小颜色数量称为主导的边缘数字，由$χ_{dom}^{\ prime}（g）$表示。我们获得$χ_{dom}^{\ prime}（g）$的一些属性，并将其计算为特定图形。另外，当$ g $通过在$ g $的顶点和边缘上修改$ g $时，我们还检查了$χ_{dom}^{\ prime}（g）$的影响。最后，我们考虑$ g $的$ k $ - 订阅，并研究此类图的主导的边缘数字。
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 $χ_{dom}^{\prime}(G)$. We obtain some properties of $χ_{dom}^{\prime}(G)$ and compute it for specific graphs. Also we examine the effects on $χ_{dom}^{\prime}(G)$ 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.
