Connection Numbers on Carbon Nanocone Line Graphs and Various Chemical Line Graphs

Abstract

In this study, we delve into the mathematical exploration of the Connection Number in carbon nanocone line graphs and diverse chemical line graphs within the realm of Graph Theory. The theoretical framework is developed based on the principles of connectivity and network structures. These structures are represented as graphs, where atoms constitute nodes and chemical bonds form edges. The novel metric, Connection Number, is introduced to quantify connectivity within these unique molecular configurations. Employing graph invariants and specialized connectivity indices, the study characterizes and compares the structural features of carbon nanocones and various chemical line graphs. Advanced graph algorithms are utilized to unveil the intricate relationship between Connection Number and structural stability, offering insights into the impact of connectivity on molecular properties and reactivity. The analysis extends to identifying recurring structural motifs and patterns, contributing to a systematic classification of connectivity profiles. Beyond theoretical considerations, the study explores practical applications in nanotechnology, materials science, and chemical engineering. This concise investigation harnesses the power of graph theory to deepen our understanding of molecular connectivity in carbon nanocones and diverse chemical line graphs, paving the way for innovative advancements in nanoscience and materials engineering.