Eccentricity Based Topological Invariants of Tightest non-adjacently Configured Stable Pentagonal Structure of Carbon Nanocones

Conjugated open ended cones in which the configured pentagons are consistent, lies in the circle of Fries Kekule structure [8]. This non-adjacent tightest configuration of pentagons as shown in the Fig. 1 is consistent with a Fries Kekule structure and thus provides the most stable cone. In the study, various topological indices of the same structure in regard of physico-concoction resources and bioactivity of substance mixtures are studied which further helps to study the behavior of chemical compounds. In this regard, Zagreb indices M_1^* (G) and M_2^* (G) of a molecular graph G are used to evaluate the complexity in chemical systems and biological organisms. In this manuscript, we consider two complex families of stable carbon nanocones and compute their ECI, TEI and eccentricity-based Zagreb indices.

EFFECT OF BOND ALTERNATION ON ELECTRONIC ENERGY BAND STRUCTURE OF ARMCHAIR CARBON NANOTUBES

The influence of the bond alternation on electronic energy band structure of armchair carbon nanotubes is studied by the tight-binding approximation. It is shown that the armchair carbon nanotubes at ground state with Kekule structure open small band gap at the Fermi level. Dependence of energy band gap of armchair carbon nanotubes with Kekule structure on their radius is considered and numerically calculated. The numerical calculations are applied to the (n, n) carbon nanotubes with n = 5, 6, 7, 8.

A graph-theoretical model for ballistic conduction in single-molecule conductors

The tight-binding version of the source-and-sink potential (SSP) model of ballistic conduction can be cast in a graph-theoretical form where the transmission through a molecular wire depends on four characteristic polynomials: those of the molecular graph and the vertex-deleted subgraphs with one or both of the molecular vertices contacting the electrodes removed. This gives an explicit function for the dependence of transmission on energy, one that is well adapted for qualitative description of general classes of conductors and conduction behavior. It also leads directly to a selection-rule criterion for conduction in terms of counting zero roots of the polynomials, which for benzenoids and graphenes is shown to subsume literature approaches based on Kekulé structure counting, bond order, and frontier-orbital matching. As explicitly demonstrated here, the SSP transmission function agrees with that derived by the Green’s function (GF) method.