Comparative Analysis of Subdivided Hex-Derived Networks Using Structural Descriptors

Abstract

A structural descriptor is a numeric quantity, invariant under symmetry, extracted from a molecular graph $\Gamma$ using tools from mathematics. Hex-derived networks $HDN1\left(n\right)$ and $HDN2\left.\left(n\right)\right)$ being dual of (3,12,12) and (4,8,8) carbon allotrope (nanocones, nanotubes) are quite fascinating structures in mathematical chemistry. In this paper, we compute exact formulas of various significant structure descriptors for the subdivision of the second and the third kind of hex-derived networks $SHDN2\left(n\right)$ and $SHDN3\left(n\right)$ , respectively. Moreover, we perform a comparative graphical analysis among certain descriptors of $SHDN1\left(n\right)$ , $SHDN2\left(n\right)$ , and $SHDN3\left(n\right)$ to help understand and provide an insight to anticipate some physicochemical properties of the networks under discussion.