A228309 The hyper-Wiener index of the odd graph O_n (n>=2).
3, 105, 2590, 57015, 1165626, 22834812, 433178460, 8036703675, 146451924190, 2632740298188, 46790614294788, 824017920352900, 14397367664647800, 249906966022292400, 4312825574857068600, 74063143648813911075
Offset: 2
Keywords
References
- N. Biggs, Algebraic Graph Theory, Cambridge, 2nd. Ed., 1993, p. 161.
- R. Balakrishnan, N. Sridharan and K. Viswanathan Iyer, The Wiener index of odd graphs, J. Indian. Inst. Sci., vol. 86, 2006, 527-531.
Links
- R. Balakrishnan, N. Sridharan and K. Viswanathan Iyer,, The Wiener index of odd graphs, J. Ind. Inst. Sci., vol. 86, no. 5, 2006. [Cached copy]
- Eric Weisstein's World of Mathematics, Odd Graph.
Programs
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Maple
B := proc (n) options operator, arrow: [seq(n-floor((1/2)*m), m = 1 .. n-1)] end proc: C := proc (n) options operator, arrow: [seq(ceil((1/2)*m), m = 1 .. n-1)] end proc: H := proc (n) options operator, arrow: (1/2)*binomial(2*n-1, n-1)*(sum((product(B(n)[r]/C(n)[r], r = 1 .. j))*t^j, j = 1 .. n-1)) end proc: HWi := proc (n) options operator, arrow: subs(t = 1, diff(H(n), t)+(1/2)*(diff(H(n), `$`(t, 2)))) end proc: seq(HWi(n), n = 2 .. 20);
Formula
A formula is "hidden" in the Maple program. B(n) and C(n) are the intersection arrays of O_n, H(n) is the Hosoya-Wiener polynomial of O_n, and HWi(n) is the hyper-Wiener index of O_n.
Comments