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A180577 The Wiener index of the windmill graph D(6,n). The windmill graph D(m,n) is the graph obtained by taking n copies of the complete graph K_m with a vertex in common (i.e., a bouquet of n pieces of K_m graphs). 4

%I #16 Mar 29 2020 13:09:52

%S 15,80,195,360,575,840,1155,1520,1935,2400,2915,3480,4095,4760,5475,

%T 6240,7055,7920,8835,9800,10815,11880,12995,14160,15375,16640,17955,

%U 19320,20735,22200,23715,25280,26895,28560,30275,32040,33855,35720

%N The Wiener index of the windmill graph D(6,n). The windmill graph D(m,n) is the graph obtained by taking n copies of the complete graph K_m with a vertex in common (i.e., a bouquet of n pieces of K_m graphs).

%C The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.

%C The Wiener polynomial of D(m,n) is (1/2)n(m-1)t[(m-1)(n-1)t+m].

%C The Wiener index of D(m,n) is (1/2)n(m-1)[(m-1)(2n-1)+1].

%C For the Wiener indices of D(3,n), D(4,n), and D(5,n) see A033991, A152743, and A028994, respectively.

%H B. E. Sagan, Y-N. Yeh and P. Zhang, <a href="http://users.math.msu.edu/users/sagan/Papers/Old/wpg-pub.pdf">The Wiener Polynomial of a Graph</a>, Internat. J. of Quantum Chem., 60, 1996, 959-969.

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 5n(5n-2).

%F G.f.: -5*x*(7*x+3)/(x-1)^3. - _Colin Barker_, Oct 30 2012

%p seq(5*n*(-2+5*n), n = 1 .. 40);

%o (PARI) a(n)=5*n*(5*n-2) \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A028994, A033991, A152743.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Sep 21 2010

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)