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

Let G be a finite solvable group and let ∆(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 fora 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.