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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| Published in | Polycyclic aromatic compounds Vol. 42; no. 10; pp. 6975 - 6987 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Philadelphia
Taylor & Francis
26.11.2022
Taylor & Francis Ltd |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Shabbir, Ayesha Azeem, Muhammad Nadeem, Muhammad Faisal |
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| SubjectTerms | Apexes Chemical bonds Chemical compounds cyclic hexagonal square chain Fault tolerance fault tolerant metric dimension Graph theory linear heptagons linear phenylene Metric dimension |
| Title | On Metric Dimension and Fault Tolerant Metric Dimension of Some Chemical Structures |
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