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 A228306 The Wiener index of the Kneser graph K(n,2) (n>=5). 1

%I #7 Jul 22 2022 11:20:45

%S 75,165,315,546,882,1350,1980,2805,3861,5187,6825,8820,11220,14076,

%T 17442,21375,25935,31185,37191,44022,51750,60450,70200,81081,93177,

%U 106575,121365,137640,155496,175032,196350,219555,244755,272061,301587,333450

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

%C 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.

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

%C K(5,2) is the Petersen graph.

%C 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].

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KneserGraph.html">Kneser Graph</a>.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

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

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

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

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

%Y Cf. A228307

%K nonn,easy

%O 5,1

%A _Emeric Deutsch_, Aug 20 2013

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Last modified October 4 02:45 EDT 2023. Contains 365872 sequences. (Running on oeis4.)