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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2411.15794 |
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| _version_ | 1866910712556683264 |
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| author | Cameron, Peter J. Sivanesan, G. Selvaraj, C. Chelvam, T. Tamizh Laubacher, Jacob |
| author_facet | Cameron, Peter J. Sivanesan, G. Selvaraj, C. Chelvam, T. Tamizh Laubacher, Jacob |
| contents | Let $G$ be a finite solvable group and let $Δ(G)$ be the character degree graph of $G$. In this paper, we obtain the metric dimension of certain character degree graphs. Specifically, we calculate the metric dimension for a regular character degree graph, a character degree graph with a diameter of $2$ that is not a block, a character degree graph with a diameter of $3$ that also has a cut vertex and a character degree graph with Fitting height $2.$ We also consider two related parameters, base size and adjacency dimension, and their relation to metric dimension for character degree graphs of solvable groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15794 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the metric dimension of the character degree graph of a solvable group Cameron, Peter J. Sivanesan, G. Selvaraj, C. Chelvam, T. Tamizh Laubacher, Jacob Group Theory Combinatorics 05C25 Let $G$ be a finite solvable group and let $Δ(G)$ be the character degree graph of $G$. In this paper, we obtain the metric dimension of certain character degree graphs. Specifically, we calculate the metric dimension for a regular character degree graph, a character degree graph with a diameter of $2$ that is not a block, a character degree graph with a diameter of $3$ that also has a cut vertex and a character degree graph with Fitting height $2.$ We also consider two related parameters, base size and adjacency dimension, and their relation to metric dimension for character degree graphs of solvable groups. |
| title | On the metric dimension of the character degree graph of a solvable group |
| topic | Group Theory Combinatorics 05C25 |
| url | https://arxiv.org/abs/2411.15794 |