The local metric dimension of split and unicyclic graphs
A set <em>W</em> is called a local resolving set of <em>G</em> if the distance of <em>u</em> and <em>v</em> to some elements of <em>W</em> are distinct for every two adjacent vertices <em>u</em> and <em>v</em> in <...
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| Format: | Article |
| Language: | English |
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InaCombS; Universitas Jember; dan Universitas Indonesia
2022-06-01
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| Series: | Indonesian Journal of Combinatorics |
| Subjects: | |
| Online Access: | http://www.ijc.or.id/index.php/ijc/article/view/174 |
| _version_ | 1797946199809982464 |
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| author | Dinny Fitriani Anisa Rarasati Suhadi Wido Saputro Edy Tri Baskoro |
| author_facet | Dinny Fitriani Anisa Rarasati Suhadi Wido Saputro Edy Tri Baskoro |
| author_sort | Dinny Fitriani |
| collection | DOAJ |
| description | A set <em>W</em> is called a local resolving set of <em>G</em> if the distance of <em>u</em> and <em>v</em> to some elements of <em>W</em> are distinct for every two adjacent vertices <em>u</em> and <em>v</em> in <em>G</em>. The local metric dimension of <em>G</em> is the minimum cardinality of a local resolving set of <em>G</em>. A connected graph <em>G</em> is called a split graph if <em>V</em>(<em>G</em>) can be partitioned into two subsets <em>V</em><sub>1</sub> and <em>V</em><sub>2</sub> where an induced subgraph of G by <em>V</em><sub>1</sub> and <em>V</em><sub>2</sub> is a complete graph and an independent set, respectively. We also consider a graph, namely the unicyclic graph which is a connected graph containing exactly one cycle. In this paper, we provide a general sharp bounds of local metric dimension of split graph. We also determine an exact value of local metric dimension of any unicyclic graphs. |
| first_indexed | 2024-04-10T21:07:06Z |
| format | Article |
| id | doaj.art-0012a81e32cd455b90b806b9ec1acb2f |
| institution | Directory Open Access Journal |
| issn | 2541-2205 |
| language | English |
| last_indexed | 2024-04-10T21:07:06Z |
| publishDate | 2022-06-01 |
| publisher | InaCombS; Universitas Jember; dan Universitas Indonesia |
| record_format | Article |
| series | Indonesian Journal of Combinatorics |
| spelling | doaj.art-0012a81e32cd455b90b806b9ec1acb2f2023-01-22T03:10:03ZengInaCombS; Universitas Jember; dan Universitas IndonesiaIndonesian Journal of Combinatorics2541-22052022-06-0161505710.19184/ijc.2022.6.1.371The local metric dimension of split and unicyclic graphsDinny Fitriani0Anisa Rarasati1Suhadi Wido Saputro2Edy Tri Baskoro3Institut Teknologi BandungInstitut Teknologi BandungInstitut Teknologi BandungInstitut Teknologi BandungA set <em>W</em> is called a local resolving set of <em>G</em> if the distance of <em>u</em> and <em>v</em> to some elements of <em>W</em> are distinct for every two adjacent vertices <em>u</em> and <em>v</em> in <em>G</em>. The local metric dimension of <em>G</em> is the minimum cardinality of a local resolving set of <em>G</em>. A connected graph <em>G</em> is called a split graph if <em>V</em>(<em>G</em>) can be partitioned into two subsets <em>V</em><sub>1</sub> and <em>V</em><sub>2</sub> where an induced subgraph of G by <em>V</em><sub>1</sub> and <em>V</em><sub>2</sub> is a complete graph and an independent set, respectively. We also consider a graph, namely the unicyclic graph which is a connected graph containing exactly one cycle. In this paper, we provide a general sharp bounds of local metric dimension of split graph. We also determine an exact value of local metric dimension of any unicyclic graphs.http://www.ijc.or.id/index.php/ijc/article/view/174local basis, local metric dimension, local resolving set, split graph, unicyclic graph |
| spellingShingle | Dinny Fitriani Anisa Rarasati Suhadi Wido Saputro Edy Tri Baskoro The local metric dimension of split and unicyclic graphs Indonesian Journal of Combinatorics local basis, local metric dimension, local resolving set, split graph, unicyclic graph |
| title | The local metric dimension of split and unicyclic graphs |
| title_full | The local metric dimension of split and unicyclic graphs |
| title_fullStr | The local metric dimension of split and unicyclic graphs |
| title_full_unstemmed | The local metric dimension of split and unicyclic graphs |
| title_short | The local metric dimension of split and unicyclic graphs |
| title_sort | local metric dimension of split and unicyclic graphs |
| topic | local basis, local metric dimension, local resolving set, split graph, unicyclic graph |
| url | http://www.ijc.or.id/index.php/ijc/article/view/174 |
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