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