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A228310
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The hyper-Wiener index of the hypercube graph Q(n) (n>=2).
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0
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10, 72, 448, 2560, 13824, 71680, 360448, 1769472, 8519680, 40370176, 188743680, 872415232, 3992977408, 18119393280, 81604378624, 365072220160, 1623497637888, 7181185318912, 31610959298560, 138538465099776, 604731395276800, 2630031813640192
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OFFSET
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2,1
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COMMENTS
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The hypercube graph Q(n) has as vertices the binary words of length n and an edge joins two vertices whenever the corresponding binary words differ in just one place.
Q(n) is distance-transitive and therefore also distance-regular. The intersection array is {n,n-1,n-2,...,1; 1,2,3,...,n-1,n}.
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REFERENCES
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Norman Biggs, Algebraic Graph Theory, 2nd ed. Cambridge University Press, 1993 (p. 161).
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LINKS
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FORMULA
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a(n) = 4^{n-2}*n*(3+n).
G.f.: 2*x^2*(5 - 24*x + 32*x^2)/(1-4*x)^3.
The Hosoya-Wiener polynomial of Q(n) is 2^{n-1}*((1+t)^n - 1).
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MAPLE
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a := proc (n) options operator, arrow: 4^(n-2)*n*(3+n) end proc: seq(a(n), n = 2 .. 25);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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