Metric Dimension of Generalized Theta Graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912645946277888 |
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| author | Benakli, Nadia Froitzheim, Nicole Martinez, David |
| author_facet | Benakli, Nadia Froitzheim, Nicole Martinez, David |
| contents | A vertex $w$ in a graph $G$ is said to resolve two vertices $u$ and $v$ if $d(w,u)\neq d(w, v)$. A set $W$ of vertices is a resolving set for $G$ if every pair of distinct vertices is resolved by some vertex in $W$. The metric dimension of $G$ is the minimum cardinality of such a set. In this paper, we investigate the metric dimension of generalized theta graphs, providing exact values and structural insights for several subclasses. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12100 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Metric Dimension of Generalized Theta Graphs Benakli, Nadia Froitzheim, Nicole Martinez, David Combinatorics 05C12 A vertex $w$ in a graph $G$ is said to resolve two vertices $u$ and $v$ if $d(w,u)\neq d(w, v)$. A set $W$ of vertices is a resolving set for $G$ if every pair of distinct vertices is resolved by some vertex in $W$. The metric dimension of $G$ is the minimum cardinality of such a set. In this paper, we investigate the metric dimension of generalized theta graphs, providing exact values and structural insights for several subclasses. |
| title | Metric Dimension of Generalized Theta Graphs |
| topic | Combinatorics 05C12 |
| url | https://arxiv.org/abs/2510.12100 |