On the Metric Dimension of Generalized Tensor Product of Interval with Paths and Cycles
The concept of minimum resolving set for a connected graph has played a vital role in Robotic navigation, networking, and in computer sciences. In this article, we investigate the values of m and n for which P2⊗mPn and P2⊗mCn are connected and find metric dimension in this case. We also conclude tha...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/2168713 |
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| _version_ | 1832566402946433024 |
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| author | Song Li Jia-Bao Liu Mobeen Munir |
| author_facet | Song Li Jia-Bao Liu Mobeen Munir |
| author_sort | Song Li |
| collection | DOAJ |
| description | The concept of minimum resolving set for a connected graph has played a vital role in Robotic navigation, networking, and in computer sciences. In this article, we investigate the values of m and n for which P2⊗mPn and P2⊗mCn are connected and find metric dimension in this case. We also conclude that, for each m, we obtain a new regular family of constant metric dimension. We also give a basis for these graphs and presentation of resolving vector in general closed form with respect to the basis. |
| format | Article |
| id | doaj-art-539fe526d2e5472591fe9d0fb7225d92 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-539fe526d2e5472591fe9d0fb7225d922025-02-03T01:04:08ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/21687132168713On the Metric Dimension of Generalized Tensor Product of Interval with Paths and CyclesSong Li0Jia-Bao Liu1Mobeen Munir2School of Computer Science and Technology, Hefei Normal University, Anhui, Hefei 230601, ChinaSchool of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaDepartment of Mathematics, Division of Science and Technology, University of Education, Lahore, PakistanThe concept of minimum resolving set for a connected graph has played a vital role in Robotic navigation, networking, and in computer sciences. In this article, we investigate the values of m and n for which P2⊗mPn and P2⊗mCn are connected and find metric dimension in this case. We also conclude that, for each m, we obtain a new regular family of constant metric dimension. We also give a basis for these graphs and presentation of resolving vector in general closed form with respect to the basis.http://dx.doi.org/10.1155/2020/2168713 |
| spellingShingle | Song Li Jia-Bao Liu Mobeen Munir On the Metric Dimension of Generalized Tensor Product of Interval with Paths and Cycles Journal of Mathematics |
| title | On the Metric Dimension of Generalized Tensor Product of Interval with Paths and Cycles |
| title_full | On the Metric Dimension of Generalized Tensor Product of Interval with Paths and Cycles |
| title_fullStr | On the Metric Dimension of Generalized Tensor Product of Interval with Paths and Cycles |
| title_full_unstemmed | On the Metric Dimension of Generalized Tensor Product of Interval with Paths and Cycles |
| title_short | On the Metric Dimension of Generalized Tensor Product of Interval with Paths and Cycles |
| title_sort | on the metric dimension of generalized tensor product of interval with paths and cycles |
| url | http://dx.doi.org/10.1155/2020/2168713 |
| work_keys_str_mv | AT songli onthemetricdimensionofgeneralizedtensorproductofintervalwithpathsandcycles AT jiabaoliu onthemetricdimensionofgeneralizedtensorproductofintervalwithpathsandcycles AT mobeenmunir onthemetricdimensionofgeneralizedtensorproductofintervalwithpathsandcycles |