On the Sombor index of corona product of certain graphs and honeycomb networks

Abstract

Topological indices are critical components in mathematical chemistry because they help in the determination of structure information that can be used in predicting physical and chemical attributes of molecules using the principles of QSAR/QSPR. Unlike the traditional indices such as the Randic index or Zagreb index, Sombor index has emerged popular due to its potential to quantify structural diversity through Pythagorean-based degree mixing. To facilitate modeling of complex structures with repeating patterns such as honeycomb lattices, which play an integral role in developing large-scale networks, this paper explores the characteristics of the Sombor index within the context of corona graph product. Such structures have proved critical in the field of studying allotropes of carbon, especially graphene and nanoribbons. For predicting the level of fractionalization and growth of these honeycomb structures, it is vital to move away from the analysis of individual replacements and conduct a complete structural analysis of the corona product. The computation of indices for these growths can be highly computational even though the corona product has an essential role in generating graph structures from smaller parts. In this research, it is demonstrated that there exists a general theorem that only considers the parameters of order, size, and degree sequence of the component graphs for calculating the Sombor index of the corona product. This result is a valuable model in chemical graph theory and machine learning as it presents a compact mathematical formulation for studying the structural characteristics of complex modules and honeycomb-like nano-structures.