A228306 The Wiener index of the Kneser graph K(n,2) (n>=5).

75, 165, 315, 546, 882, 1350, 1980, 2805, 3861, 5187, 6825, 8820, 11220, 14076, 17442, 21375, 25935, 31185, 37191, 44022, 51750, 60450, 70200, 81081, 93177, 106575, 121365, 137640, 155496, 175032, 196350, 219555, 244755, 272061, 301587, 333450

Offset

5,1

Comments

The Kneser graph K(n,2) is the graph whose vertices represent the 2-subsets of {1,2,...,n} and two vertices are connected if and only if they correspond to disjoint subsets.

K(n,2) is disconnected for n<=4.

K(5,2) is the Petersen graph.

The Kneser graph K(n,2) is distance-regular with intersection array [(n-2)*(n-3)/2, 2*(n-4); 1, (n-3)*(n-4)/2].

References

R. Balakkrishnan, S. Francis Raj, The Wiener number of Kneser graphs, Discussiones Math, Graph Theory, 28, 2008, 219-228.

Links

Table of n, a(n) for n=5..40.

Eric Weisstein's World of Mathematics, Kneser Graph.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = (1/8)*n*(n-1)*(n-2)*(n+5).

G.f.: 3*x^5*(25-70*x+80*x^2-43*x^3+9*x^4)/(1-x)^5.

The Hosoya-Wiener polynomial of K(n,2) is (1/8)*n*(n-1)*(n-2)*t*(n-3+4*t).

Maple

a := proc (n) options operator, arrow: (1/8)*n*(n-1)*(n-2)*(n+5) end proc: seq(a(n), n = 5 .. 40);

Crossrefs

Cf. A228307

Sequence in context: A023095 A044326 A044707 * A044407 A044788 A003503

Adjacent sequences: A228303 A228304 A228305 * A228307 A228308 A228309

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 20 2013

Status

approved