Boron clusters sheets with algebraic properties

Abstract

Boron clusters are small, three-dimensional structures made of boron atoms. These come in a wide range of shapes and sizes, from basic planar constructions to complex polyhedral patterns. Boron clusters are fascinating from both a fundamental and practical perspective because of their unique electrical, optical, and chemical properties. More focus has lately been placed on boron cluster sheets, which are two-dimensional structures made of boron clusters. Quantitative structure-activity relationship (QSAR) studies implement M-polynomials, a type of molecular descriptor, to describe the topology of molecules. These are based on the notion of graph theory, which provides a theoretical framework for quantitatively studying molecular graphs. In this article, we discussed some novel topological descriptors-based M-polynomials and found algebraic formulations for the boron cluster or borophene sheets. We discussed first Zagreb, second Zagreb and Randić M-polynomials, based on the different differential and integral operators.