Topological Aspects of Molecular Networks: Crystal Cubic Carbons

Abstract

Theory of networks serves as a mathematical foundation for the construction and modeling of chemical structures and complicated networks. In particular, chemical networking theory has a wide range of utilizations in the study of chemical structures, where examination and manipulation of chemical structural information are made feasible by utilizing the numerical graph invariants. A network invariant or a topological index (TI) is a numerical measure of a chemical compound which is capable to describe the chemical structural properties such as melting point, freezing point, density, pressure, tension, and temperature of chemical compounds. Wiener initiated the first distance-based TI which is considered to be the most important TI to preserve the chemical and physical properties of chemical structures. Later on, degree-based TI was introduced to find the $\pi$ -electron energy of molecules. Recently, connection number-based TIs are studied which are more efficient than degree and distance-based TIs. In this paper, we compute the connection number-based TIs of the structure of crystal cubic carbons which are one of the most significant and interesting composites in modern resources of science due to the involvement of carbon atoms.