On Metric Dimension and Fault Tolerant Metric Dimension of Some Chemical Structures

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 is an ordered subset of vertices of a graph G, in which each vertex of G is distinctively determined by its distance to...

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Bibliographic Details
Published inPolycyclic aromatic compounds Vol. 42; no. 10; pp. 6975 - 6987
Main Authors Nadeem, Muhammad Faisal, Shabbir, Ayesha, Azeem, Muhammad
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 26.11.2022
Taylor & Francis Ltd
Subjects
Apexes
Chemical bonds
Chemical compounds
cyclic hexagonal square chain
Fault tolerance
fault tolerant metric dimension
Graph theory
linear heptagons
linear phenylene
Metric dimension
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Summary: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 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 The cardinality of a minimum resolving set is called the metric dimension of G. A resolving set of G is fault-tolerant if is also a resolving set, for every v in 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.
ISSN:1040-6638
1563-5333
DOI:10.1080/10406638.2021.1994429