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

2,1

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