Metric dimension of cycloparaphenylene and its derived molecular structures

A chemical graph is a mathematical depiction of a chemical molecule utilizing graph theory. It abstracts molecules by representing atoms as vertices and chemical bonds as edges. Each atom can be distinctly identified by measuring distances to a limited collection of reference atoms known as the resolving set, the minimal cardinality of which is referred to as the metric dimension. This parameter can aid in differentiating isomers or examining molecular symmetry. Highly symmetric molecules typically exhibit reduced metric dimensions, as fewer vertices are required to distinctly define all positions, which is advantageous in cheminformatics. This parameter is investigated for cycloparaphenylene, pyrene-containing π-extended carbon nanorings, cycloparaphenylene nanorings functionalised with graphenic hexabenzocoronene sidewalls, and polythiophene molecular structures.