  In this paper extremal values of the difference between several graph
invariants related to the metric dimension are studied: mixed metric dimension,
edge metric dimension and strong metric dimension. These non-trivial extremal
values are computed over all connected graphs of given order. To obtain such
extremal values several techniques are developed. They use functions related to
metric dimension graph invariants to obtain lower and/or upper bounds on these
extremal values and exact computations when restricting to some specific
families of graphs.
