Metric, edge-metric, mixed-metric, and fault-tolerant metric dimensions of geometric networks with potential applications

Abstract

Resolvability parameters of graphs are widely applicable in fields like computer science, chemistry, and geography. Many of these parameters, such as the metric dimension, are computationally hard to determine. This paper focuses on Möbius-type geometric graphs, including hexagonal Möbius graphs, barycentric subdivisions of Möbius ladders, and octagonal Möbius chains. It addresses several open problems related to their resolvability parameters, such as the exchange property and fault-tolerant metric dimension. Additionally, the study extends to 30 lower benzenoid hydrocarbons, computing their metric, edge metric, and mixed metric dimensions. These results support structure-property modeling, particularly for predicting the total -electronic energy of such hydrocarbons. The paper concludes with new questions prompted by the findings.