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.
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
KEYWORD
nonn
AUTHOR
Nilanjan De, Jun 08 2014
STATUS
approved