The Metric Dimension and Local Metric Dimension of Relative Prime Graph
This study aims to determine the value of metric dimensions and local metric dimensions of relative prime graphs formed from modulo integer rings, namely . As a vertex set is and if and are relatively prime. By finding the pattern elements of resolving set and local resolving set, it can be sho...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Mathematics Department UIN Maulana Malik Ibrahim Malang
2020-11-01
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| Series: | Cauchy: Jurnal Matematika Murni dan Aplikasi |
| Subjects: | |
| Online Access: | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/10103 |
| _version_ | 1811337845934129152 |
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| author | Inna Kuswandari Fatmawati Fatmawati Mohammad Imam Utoyo |
| author_facet | Inna Kuswandari Fatmawati Fatmawati Mohammad Imam Utoyo |
| author_sort | Inna Kuswandari |
| collection | DOAJ |
| description | This study aims to determine the value of metric dimensions and local metric dimensions of relative prime graphs formed from modulo integer rings, namely . As a vertex set is and if and are relatively prime. By finding the pattern elements of resolving set and local resolving set, it can be shown the value of the metric dimension and the local metric dimension of graphs are and respectively, where is the number of vertices groups that formed multiple 2,3, … , and is the cardinality of set . This research can be developed by determining the value of the fractional metric dimension, local fractional metric dimension and studying the advanced properties of graphs related to their forming rings.
Key Words : metric dimension; modulo ; relative prime graph; resolving set; rings. |
| first_indexed | 2024-04-13T18:01:56Z |
| format | Article |
| id | doaj.art-a4665aaf413f497b9bba49b468dcfd58 |
| institution | Directory Open Access Journal |
| issn | 2086-0382 2477-3344 |
| language | English |
| last_indexed | 2024-04-13T18:01:56Z |
| publishDate | 2020-11-01 |
| publisher | Mathematics Department UIN Maulana Malik Ibrahim Malang |
| record_format | Article |
| series | Cauchy: Jurnal Matematika Murni dan Aplikasi |
| spelling | doaj.art-a4665aaf413f497b9bba49b468dcfd582022-12-22T02:36:14ZengMathematics Department UIN Maulana Malik Ibrahim MalangCauchy: Jurnal Matematika Murni dan Aplikasi2086-03822477-33442020-11-016314916110.18860/ca.v6i3.101035316The Metric Dimension and Local Metric Dimension of Relative Prime GraphInna Kuswandari0Fatmawati Fatmawati1Mohammad Imam Utoyo2UNIVERSITAS AIRLANGGAUniversitas AirlanggaUniversitas AirlanggaThis study aims to determine the value of metric dimensions and local metric dimensions of relative prime graphs formed from modulo integer rings, namely . As a vertex set is and if and are relatively prime. By finding the pattern elements of resolving set and local resolving set, it can be shown the value of the metric dimension and the local metric dimension of graphs are and respectively, where is the number of vertices groups that formed multiple 2,3, … , and is the cardinality of set . This research can be developed by determining the value of the fractional metric dimension, local fractional metric dimension and studying the advanced properties of graphs related to their forming rings. Key Words : metric dimension; modulo ; relative prime graph; resolving set; rings.https://ejournal.uin-malang.ac.id/index.php/Math/article/view/10103graph theory |
| spellingShingle | Inna Kuswandari Fatmawati Fatmawati Mohammad Imam Utoyo The Metric Dimension and Local Metric Dimension of Relative Prime Graph Cauchy: Jurnal Matematika Murni dan Aplikasi graph theory |
| title | The Metric Dimension and Local Metric Dimension of Relative Prime Graph |
| title_full | The Metric Dimension and Local Metric Dimension of Relative Prime Graph |
| title_fullStr | The Metric Dimension and Local Metric Dimension of Relative Prime Graph |
| title_full_unstemmed | The Metric Dimension and Local Metric Dimension of Relative Prime Graph |
| title_short | The Metric Dimension and Local Metric Dimension of Relative Prime Graph |
| title_sort | metric dimension and local metric dimension of relative prime graph |
| topic | graph theory |
| url | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/10103 |
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