On Metric Dimension and Fault Tolerant Metric Dimension of Some Chemical Structures
Muhammad Faisal Nadeem, Ayesha Shabbir, Muhammad Sohaib Azeem · Polycyclic aromatic compounds · 2021
In chemistry, customary depiction for the structure of chemical compounds are graphs where the vertices and edges represents the atoms and bonds types, respectively. Resolving set ℵ is an ordered subset of vertices of a graph G, in which each vertex of G is distinctively determined by its distance to the vertices in ℵ. The cardinality of a minimum resolving set is called the metric dimension of G. A resolving set ℵf of G is fault-tolerant if ℵf∖v is also a resolving set, for every v in ℵf. Resolving set allows to obtain a unique representation for chemical structures. In particular, they were used in pharmaceutical research for discovering patterns common to a variety of drugs. In this paper we determine the exact metric and fault tolerant metric dimension of cyclic hexagonal square chain, linear phenylene, and linear heptagons structure.