The Number of Coloured Graphs
L. Carlitz · Canadian Journal of Mathematics · 1963
Let Fn(k) denote the total number of k-coloured graphs on n labelled nodes and let Mn(k) denote the number of graphs on n nodes that are coloured in at most kcolours ; also let fn(k) denote the number of connected k coloured graphs on n nodes. Read (3) has proved the following formulas: