Coloring in graphs of twist knots

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.