# Colouring Graphs: Identifying Chromatic Number

So I'm asked to find the chromatic number for the given graph by colouring the vertices using the minimum number of required colours. My attempt at doing so is below but I was wondering if someone could confirm whether I coloured it correctly? Are there any vertices that should be a different colour/should there be more or less colours used? Did I misplace any colours?

I was also wondering if there is some rule or formula to figure out the chromatic number for a graph?

I'd appreciate some help or confirmation.

Nodes $$8, 14, 15$$ form a triangle. Therefore it is not possible to color the graph with less than $$3$$ colors. Since you used $$3$$ colors and no two adjacent nodes have the same color, your coloring is correct.