A242371 Modified eccentric connectivity index of the cycle graph with n vertices, C[n].

12, 32, 40, 72, 84, 128, 144, 200, 220, 288, 312, 392, 420, 512, 544, 648, 684, 800, 840, 968, 1012, 1152, 1200, 1352, 1404, 1568, 1624, 1800, 1860, 2048, 2112, 2312, 2380, 2592, 2664, 2888, 2964, 3200, 3280, 3528, 3612, 3872, 3960, 4232, 4324, 4608, 4704

Offset

3,1

Comments

The modified eccentric connectivity index of a graph is defined as the sum of the products of eccentricity with the total degree of neighboring vertices, over all vertices of the graph. This is a generalization of eccentric connectivity index.

a(n) = 4*A093353(n-1) = n*A168273(n) for n>2. - Alois P. Heinz, Jun 26 2014

Links

Nilanjan De, Table of n, a(n) for n = 3..100

N. De, S. M. A. Nayeem and A. Pal, Bounds for modified eccentric connectivity index, Advanced Modeling and Optimization, 16(1) (2014) 133-142.

N. De, S. M. A. Nayeem and A. Pal, Bounds for modified eccentric connectivity index, arXiv:1402.1870 [math.CO], 2014.

Eric Weisstein's World of Mathematics, Graph Eccentricity

Formula

a(n) = 2*n*(n-1) if n is odd; and a(n) = 2*n^2 if n is even (n>2).

G.f.: -4*x^3*(3+5*x-4*x^2-2*x^3+2*x^4)/((x+1)^2*(x-1)^3). - Alois P. Heinz, Jun 26 2014

Example

a(3) = 3*4 = 12 because there are 3 vertices and each vertex has eccentricity 1 and the total degree of neighboring vertices is 4.

Maple

a:= n-> n*(2*n-1+(-1)^n):
seq(a(n), n=3..60);  # Alois P. Heinz, Jun 26 2014

Mathematica

a[n_] := 2n(n-Boole[OddQ[n]]);
Table[a[n], {n, 3, 50}] (* Jean-François Alcover, Nov 28 2018 *)

Prog

(PARI) a(n) = if (n % 2, 2*n*(n-1), 2*n^2); \\ Michel Marcus, Jun 20 2014

Crossrefs

Cf. A093353, A168273, A206490, A238410, A238411.

Sequence in context: A031118 A335100 A334606 * A118785 A071336 A248817

Adjacent sequences: A242368 A242369 A242370 * A242372 A242373 A242374

Keyword

nonn

Author

Nilanjan De, Jun 08 2014

Status

approved