The eccentric connectivity index of armchair polyhex nanotubes

Abstract

The eccentric connectivity index ξ(G) of the graph G is defined as ξ(G) = Σu∈V(G) deg(u)ε(u) where deg(u) denotes the degree of vertex u and ε(u) is the largest distance between u and any other vertex v of G. In this paper an exact expression for the eccentric connectivity index of an armchair polyhex nanotube is given.

Augmented eccentric connectivity index

“…The distances (and hence the eccentricities) relevant for our purpose were computed in a paper dealing with the eccentric connectivity index of armchair nanotubes [10]. By using those results we can derive explicit formulas for A .N.r; s// in terms of r and s. The exact expressions depend on the relationship between those two parameters.…”

Eccentric Connectivity Index of t-Polyacenic Nanotubes

“…Also, this index has been proved to provide a high degree of predictability with regard to anticonvulsant activity [20] in comparison to Zagreb indices. Recently, the eccentric connectivity index has been studied for certain nanotubes [21][22][23][24][25][26] and for several molecular graphs [27][28][29].…”