On the Metric Dimension of Generalized Petersen Multigraphs
In this paper, we study the metric dimension of barycentric subdivision of Möbius ladders and the metric dimension of generalized Petersen multigraphs. We prove that the generalized Petersen multigraphs denoted by <inline-formula> <tex-math notation="LaTeX">$P(2n,n)$...
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| Autores principales: | , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
IEEE
2018
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/1147376d8c65451287f91897c0cb7fcd |
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| Sumario: | In this paper, we study the metric dimension of barycentric subdivision of Möbius ladders and the metric dimension of generalized Petersen multigraphs. We prove that the generalized Petersen multigraphs denoted by <inline-formula> <tex-math notation="LaTeX">$P(2n,n)$ </tex-math></inline-formula> have metric dimension 3 when <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is even and 4 otherwise. We also study the exchange property for resolving sets of barycentric subdivisions of Möbius ladders and generalized Petersen multigraphs and prove that the exchange property of the bases in a vector space does not hold for minimal resolving sets of these graphs. |
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