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arXiv · 2411.15794

On the metric dimension of the character degree graph of a solvable group

Peter J. Cameron·G. Sivanesan·C. Selvaraj·T. Tamizh Chelvam·Jacob Laubacher
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Abstract

Let $G$ be a finite solvable group and let $\Delta(G)$ 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.

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Peter J. Cameron, G. Sivanesan, C. Selvaraj, T. Tamizh Chelvam, Jacob Laubacher. 2024-11-24. On the metric dimension of the character degree graph of a solvable group. https://arxiv.org/abs/2411.15794

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