I have problem stating "Find total number of ways to color a regular pentagon with 5 colors." If we consider(Exact 5 colors to color the graph) it unlabeled graph then it will be the same to arranging 5 persons around a circular table where chairs are not numbered that is (5-1)!. But for labeled graph i am confused for this pentagon we can color first vertex with 5 and second with 4 and third with 3 so on .. so it is 5!(Wrong!), I think it is recursive problem.
But these are number of ways with exact 5 colors and i am also not sure my approach is correct or not ? Please suggest a good source or hint to learn general solutions for such coloring problems.
My question- "Find total number of ways to color a regular pentagon with 5 colors." It is possible with at least 3 of 5 in general so what is general solution?.