In particular I'm interested in regular maps, excluding all maps that can be colored with 2 or 3 colors. For what I need to analyze, maps have to be regarded as differently colored, if the same coloring cannot be obtained by subsequent exchanges of colors. In other words, for example, once a map has been properly colored, I don't want to count all other configurations that derive from subsequent exchanges of colors.
Since the arbitrary nature of choosing colors, these derived configurations are equivalent (for what I'm analyzing) to the first one, since they could have been obtained just choosing different colors in the first place. Instead, there are colorings that differ in such a way that exchanging colors won't help to transform one configuration into the other. In the following picture the graphs named (A) and (B) are the only ones that cannot be converted into one another by swapping colors.
My question is: how many "different" colorings (in the meaning I explained) exist for a given map? I've only found an article on http://en.wikipedia.org/wiki/Graph_coloring that count all possible colorings including swaps. Is there a paper that can help me on this?
I already posted this to math.stackexchange but, so far, I haven't received the answer I was looking for.