Compare fault-tolerance and maximum-degree growth rates

Determine for which variants xdim(G) of metric dimension the exponential growth rate of the maximum fault-tolerant parameter ftxdim(G) equals the exponential growth rate of the maximum degree Δ(G), as expressed by the limit identity posed in the paper.

Background

The paper observes that, for the variants it studies, the maximum fault-tolerant dimension grows on essentially the same exponential scale as the maximum degree. The authors ask whether this correspondence holds for other variants of metric dimension, thereby seeking a general classification of variants for which the two asymptotic rates coincide.