Abstract
There has been a recent debate that boron nanotubes can outperform carbon nanotubes on many grounds. The most stable boron nanotubes are made of a hexagonal lattice with an extra atom added to some of the hexagons called ∝-boron nanotubes. Closed forms of M-polynomial of nanotubes produce closed forms of many degree-based topological indices which are numerical parameters of the structure and determine physico-chemical properties of the concerned nanotubes. In this article, we compute and analyze many topological indices of ∝-boron nanotubes correlating with the size of structure of these tubes through the use of M-polynomial. More importantly we make a graph-theoretic comparison of indices of two types of boron nanotubes namely triangular boron and ∝-boron nanotubes.
Highlights
Mathematical chemistry provides tools such as polynomials and functions to capture information hidden in the symmetry of molecular graphs and predict properties of compounds without using quantum mechanics
As for as structure of both tubes are concerned, ∝- Boron nanotube is more complicated than Triangular boron nanotubes with addition of an extra atom to the center of some of the hexagons[15]
Values drastically increases as Χ → ±1, Y → ±2 For the most part of [−1, 1] × [−2, 2], values remain stable whereas triangular boron nanotubes show opposite trends[11], shown in Fig. 6 below
Summary
Mathematical chemistry provides tools such as polynomials and functions to capture information hidden in the symmetry of molecular graphs and predict properties of compounds without using quantum mechanics. We compute general form of M-polynomial for ∝- boron nanotube. We derive closed forms of many degree-based topological indices for these tubes.
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