Chromatic Polynomials

A coloring of the vertices of a graph is an assignment of or fewer colors to the vertices of so that no two adjacent vertices get the same color. The chromatic polynomial of is a polynomial giving the number of distinct colorings of . If has vertices, is monic (the coefficient of the highest power equals 1) of degree with integer coefficients alternating in sign and beginning , where is the number of edges of . Moreover, unless and . This Demonstration shows the chromatic polynomial corresponding to a selection of members of prominent families of graphs.

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