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A270843
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Number of nonisomorphic edge colorings of the Petersen graph with exactly n colors.
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1
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1, 394, 122601, 8510140, 210940745, 2524556538, 17167621086, 72787256640, 202996629360, 382918536000, 492133561920, 424994169600, 236107872000, 76281004800, 10897286400
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OFFSET
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1,2
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COMMENTS
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This is zero when n is more than fifteen because only fifteen edges are available.
These are not colorings in the strict sense, since there is no requirement that adjacent edges have different colors. - N. J. A. Sloane, Mar 28 2016
The value for n=15 is 15!/120 because all orbits are the same size namely 120 (order of the symmetric group on five elements) when each of the 15 edges has a unique color. - Marko Riedel, Mar 28 2016
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LINKS
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FORMULA
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Cycle index of the automorphisms acting on the edges is (1/120)*S[1]^15+(5/24)*S[2]^6*S[1]^3+(1/4)*S[4]^3*S[2]*S[1]+(1/6)*S[3]^5+(1/6)*S[3]*S[6]^2+(1/5)*S[5]^3.
Inclusion-exclusion yields a(n) = sum(C(n, q)*(-1)^q*A270842(n - q), q = 0 .. n)
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CROSSREFS
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KEYWORD
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nonn,easy,fini,full
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AUTHOR
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STATUS
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approved
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