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.
