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 A228309 The hyper-Wiener index of the odd graph O_n (n>=2). 1
 3, 105, 2590, 57015, 1165626, 22834812, 433178460, 8036703675, 146451924190, 2632740298188, 46790614294788, 824017920352900, 14397367664647800, 249906966022292400, 4312825574857068600, 74063143648813911075 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The odd graph O_n is a graph whose vertices represent the (n-1)-subsets of {1,2,...,2n-1} and two vertices are connected if and only if they correspond to disjoint subsets. It is a distance regular graph. 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 Table of n, a(n) for n=2..17. 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. 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. 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); CROSSREFS Cf. A136328, A228308 Sequence in context: A233251 A279303 A103037 * A215945 A350986 A075528 Adjacent sequences: A228306 A228307 A228308 * A228310 A228311 A228312 KEYWORD nonn AUTHOR Emeric Deutsch, Aug 20 2013 STATUS approved

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Last modified September 21 18:57 EDT 2023. Contains 365503 sequences. (Running on oeis4.)