On unicyclic graphs of metric dimension 2 with vertices of degree 4
We show that if \(G\) is a unicyclic graph with metric dimension \(2\) and \(\{a,b\}\) is a metric basis of \(G\) then the degree of any vertex \(v\) of \(G\) is at most \(4\) and degrees of both \(a\) and \(b\) are at most \(2\). The constructions of unispider and semiunispider graphs and their k...
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| Date: | 2019 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2019
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1265 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | We show that if \(G\) is a unicyclic graph with metric dimension \(2\) and \(\{a,b\}\) is a metric basis of \(G\) then the degree of any vertex \(v\) of \(G\) is at most \(4\) and degrees of both \(a\) and \(b\) are at most \(2\). The constructions of unispider and semiunispider graphs and their knittings are introduced. Using these constructions all unicyclic graphs of metric dimension \(2\) with vertices of degree \(4\) are characterized. |
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