Distance and Eccentricity Based Invariants of Certain Networks, Nanotubes, Nanotori and Fullerene

Abstract

Topological indices are numerical parameters to associate with graphs of networks, nanotube, nanotri etc and help us to understand the properties of concerned structures. These numbers remain invariant upto graph isomorphism. Like topological indices, algebraic polynomials are also important invariants to understand the topology of underlined structures and help us to recover many topological indices directly. In this thesis, we computed Hosoya, Harary and eccentricity connectivity polynomials of triangular oxide, regular triangular oxide, silicate, regular silicate networks, TUC nanotori and fullerenes. Moreover, Wiener, modified Wiener, hyper-Wiener, multiplicative Wiener, Harary and eccentric indices of above mentioned structures are also computed in this thesis. Our results may help to develop a better understanding about the nanomaterials and can be used to enhance the ability of existing nanostructures/networks.