Let T_n be a twist knot with n half-twists and G_n be the graph of T_n. The closed neighborhood N[v] of a vertex v in G_n, which included at least one colored vertex for each color in a proper n-coloring of G_n, is called a rainbow neighborhood. There are different types of graph coloring in the literature. We consider some of these types in here. In this paper, we determine the chromatic number of graphs of twist knots and study rainbow neighborhood of graphs of twist knots. We determine the rainbow neighborhood number and the fading number of them. Furthermore, we determine coupon coloring and the coupon coloring number of graphs of twist knots.

中文翻译：

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麻花结图中的着色

令T _n是具有n 个半捻的麻花结，而G _n是T _n的图。G n 中一个顶点 v 的封闭邻域 N [ v ]，它包括 G _n的适当n着色中每种颜色的_至少一个彩色顶点，称为彩虹邻域。文献中有不同类型的图形着色。我们在这里考虑其中的一些类型。在本文中，我们确定了扭结图的色数并研究了扭结图的彩虹邻域。我们确定彩虹邻域数和它们的衰落数。此外，我们确定优惠券着色和捻结图的优惠券着色数。