This paper initiates a study on the problem of computing the difference between
the metric dimension and the determining number of graphs. We provide new proofs
and results on the determining number of trees and Cartesian products of graphs,
and establish some lower bounds on the difference between the two parameters.
Cáceres, J. [et al.]. On the determining number and the metric dimension of graphs. "Electronic journal of combinatorics", 19 Abril 2010, vol. 17, núm. 1, p. 1-20.