Computing vertex resolvability of benzenoid tripod structure
In this paper, we determine the exact metric and fault-tolerant metric dimension of the benzenoid tripod structure. We also computed the generalized version of this parameter and proved that all the parameters are constant. Resolving set L is an ordered subset of nodes of a graph C, in which each ve...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022387?viewType=HTML |
| _version_ | 1818284999652147200 |
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| author | Maryam Salem Alatawi Ali Ahmad Ali N. A. Koam Sadia Husain Muhammad Azeem |
| author_facet | Maryam Salem Alatawi Ali Ahmad Ali N. A. Koam Sadia Husain Muhammad Azeem |
| author_sort | Maryam Salem Alatawi |
| collection | DOAJ |
| description | In this paper, we determine the exact metric and fault-tolerant metric dimension of the benzenoid tripod structure. We also computed the generalized version of this parameter and proved that all the parameters are constant. Resolving set L is an ordered subset of nodes of a graph C, in which each vertex of C is distinctively determined by its distance vector to the nodes in L. The cardinality of a minimum resolving set is called the metric dimension of C. A resolving set Lf of C is fault-tolerant if Lf∖b is also a resolving set, for every b in Lf. 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. The above definitions are based on the hypothesis of chemical graph theory and it is a customary depiction of chemical compounds in form of graph structures, where the node and edge represents the atom and bond types, respectively. |
| first_indexed | 2024-12-13T01:01:44Z |
| format | Article |
| id | doaj.art-a08ca482849b4fb385bec47ab2b2f07a |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-13T01:01:44Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a08ca482849b4fb385bec47ab2b2f07a2022-12-22T00:04:39ZengAIMS PressAIMS Mathematics2473-69882022-01-01746971698310.3934/math.2022387Computing vertex resolvability of benzenoid tripod structureMaryam Salem Alatawi0Ali Ahmad1Ali N. A. Koam2Sadia Husain3Muhammad Azeem41. Department of Mathematics Faculty of Sciences, University of Tabuk 71491 Tabuk, Saudi Arabia2. College of Computer Science and Information Technology, Jazan University, Jazan, Saudi Arabia3. Department of Mathematics, College of Science, Jazan University, New Campus, Jazan 2097, Saudi Arabia2. College of Computer Science and Information Technology, Jazan University, Jazan, Saudi Arabia4. Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, PakistanIn this paper, we determine the exact metric and fault-tolerant metric dimension of the benzenoid tripod structure. We also computed the generalized version of this parameter and proved that all the parameters are constant. Resolving set L is an ordered subset of nodes of a graph C, in which each vertex of C is distinctively determined by its distance vector to the nodes in L. The cardinality of a minimum resolving set is called the metric dimension of C. A resolving set Lf of C is fault-tolerant if Lf∖b is also a resolving set, for every b in Lf. 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. The above definitions are based on the hypothesis of chemical graph theory and it is a customary depiction of chemical compounds in form of graph structures, where the node and edge represents the atom and bond types, respectively.https://www.aimspress.com/article/doi/10.3934/math.2022387?viewType=HTMLnode-resolvabilityfault-tolerant node-resolvabilitybenzenoid structurebenzenoid tripod |
| spellingShingle | Maryam Salem Alatawi Ali Ahmad Ali N. A. Koam Sadia Husain Muhammad Azeem Computing vertex resolvability of benzenoid tripod structure AIMS Mathematics node-resolvability fault-tolerant node-resolvability benzenoid structure benzenoid tripod |
| title | Computing vertex resolvability of benzenoid tripod structure |
| title_full | Computing vertex resolvability of benzenoid tripod structure |
| title_fullStr | Computing vertex resolvability of benzenoid tripod structure |
| title_full_unstemmed | Computing vertex resolvability of benzenoid tripod structure |
| title_short | Computing vertex resolvability of benzenoid tripod structure |
| title_sort | computing vertex resolvability of benzenoid tripod structure |
| topic | node-resolvability fault-tolerant node-resolvability benzenoid structure benzenoid tripod |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022387?viewType=HTML |
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