Does anyone know the chromatic polynomial of the hyper cube graph Q4? I need this to verify that my listing of a subset of all DAG's on the 4-cube is correct.
Any help greatly appreciated, JC
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2$\begingroup$ Also posted on Math.SE: The chromatic polynomial of the hyper cube graph $Q_4$? $\endgroup$– Martin SleziakCommented Jun 21, 2017 at 13:50
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1 Answer
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This is what Wolfram|Alpha says:
And here it is in TeX:
$$
(x-1)
x
\left(x^{14}-3
1 x^{13}+465
x^{12}-4471
x^{11}+30793
x^{10}-160807
x^9+\\657229
x^8-2137667
x^7+5564285
x^6-11536667
x^5+\\18740317
x^4-23081607
x^3+20308039
x^2-11372201
x+3040575\right)
$$
answered Jun 21, 2017 at 13:31
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1$\begingroup$ The polynomial is also given (but not in factored form) at oeis.org/A158348 (down in the MAPLE section). $\endgroup$ Commented Jun 21, 2017 at 23:51
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2$\begingroup$ I greatly appreciate the answer, and so does my colleague. Both of us are math PhD, but not experts in graph theory. I first posted in a more general forum, but my question was put on hold. I thought the reason was that the question was of research character rather than a student's question. The answer has already been tremendously useful for a group, including students. Perhaps someone could explain what's going on. $\endgroup$– JacobCommented Jun 22, 2017 at 11:20