A Numerical Method for MEC Polynomial and MEC Index of One-Pentagonal Carbon Nanocones

Abstract

The modified eccentric connectivity (MEC) polynomial of a molecular graph, G, is defined as (G,x) = n_G(u) x^ecc(u), where ecc(u) is defined as the length of a maximal path connecting u to another vertex of molecular graph G and n_G(u) is the sum of the degrees of its neighborhoods. The MEC index is the first derivative of this polynomial for x = 1. The pentagonal carbon nanocones are constructed from a graphene sheet by removing a 60° wedge and joining the edges produces a cone with a single pentagonal defect at the apex. In this paper, we determine a numerical method for computing MEC polynomial and MEC index of one-pentagonal carbon nanocones.

Keywords:

• MEC index
• MEC polynomial
• one-pentagonal carbon nanocone
• Matlab program

Acknowledgments

The authors are indebted to the referee for his/her suggestions and helpful remarks.