Chromatic Polynomials

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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.
Contributed by: Jaime Rangel-Mondragon (August 2011)
Open content licensed under CC BY-NC-SA
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"Chromatic Polynomials"
http://demonstrations.wolfram.com/ChromaticPolynomials/
Wolfram Demonstrations Project
Published: August 16 2011