A Study on Sombor Index Across Graphs and Molecular Structures

Abstract

This doctoral thesis presents an in-depth investigation into the Sombor index, a novel degreebased newlinetopological index introduced by Ivan Gutman in late 2020. Recognizing the index s newlinepotential and addressing existing research gaps, this study aims to comprehensively explore its newlineapplications across various graph operations and molecular structures. The research is driven newlineby three primary objectives: a detailed examination of the Sombor index within different graph newlineproducts, a thorough study of its role in characterizing chemical structures, and an extensive newlineanalysis of its predictive capabilities concerning the physical properties of chemical compounds. newlineThe initial phase of the research delves into the application of the Sombor index to newlineCartesian and 2-Cartesian graph products, particularly focusing on specific regular and biregular newlinegraphs. This exploration is inspired by the significant role these graph products play newlinein communication and sensor networks. Concurrently, the study extends to tensor and 2-tensor newlinegraph products, which are prevalent in quantum information and network analysis, providing a newlinebroader understanding of the Sombor index in different mathematical contexts. Additionally, the newlineresearch investigates the index s behavior within the non-commutative Indu-Bala graph product, newlineleading to intriguing and novel findings that contribute to the field of graph theory newline