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How to calculate the ways to paint a tree's nodes with m colors so that the ends of each edge have different colors?
Any polynomial solution is welcome.
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Use only white latex paint, preferably interior grades. While exterior latex may be used, it may present a greater chance of tree damage. Oil base paints should never be used, as they are toxic to the trunk. 3.
You have m choices for the root. If you paint going down from the root, you have m-1 choices for each additional node. If the number of nodes is n, then the number of ways to paint the tree is m * (m-1)^(n-1).
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