Consider the following four graphs where $k$ represents the number of colours used to colour the vertices of each graph.
Here cycle graphs are used to represent regular polygons, in this specific case the hexagon. The tiling of interest is thus
where we are wondering about the color of each triangular tile and represent each tile with a vertex in the cycle graphs below.
I am looking for a notation similar to e.g. the Schläfli symbol (though others will do too), allowing me to refer to a specific colouring. For example, I cannot find a notation that lets me refer to the pattern in Figure (b). The Schläfli symbol for the tiling of the hexagon would be $\{3,6\}$ but is there an extension for colouring? It would seem that I require another dimension to the current notation to describe a specific colouring.
Very new to this field, any pointers would be very welcome. Thanks.