A228307 The hyper-Wiener index of the Kneser graph K(n,2) (n>=5).

105, 225, 420, 714, 1134, 1710, 2475, 3465, 4719, 6279, 8190, 10500, 13260, 16524, 20349, 24795, 29925, 35805, 42504, 50094, 58650, 68250, 78975, 90909, 104139, 118755, 134850, 152520, 171864, 192984, 215985, 240975, 268065, 297369, 329004, 363090

Offset: 5

Author

Emeric Deutsch, Aug 20 2013

Keywords

• nonn
• easy

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

• Eric Weisstein's World of Mathematics, Kneser Graph.
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A228306

Programs

Maple

a := proc (n) options operator, arrow: (1/8)*n*(n-1)*(n-2)*(n+9) end proc: seq(a(n), n = 5 .. 40);

Formula

a(n) = (1/8)*n*(n-1)*(n-2)*(n+9).

G.f.: 3*x^5*(35-100*x+115*x^2-62*x^3+13*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).

a(n) = 3*A095661(n-3). - R. J. Mathar, Aug 21 2013