A dominating set S of a graph is a metric-locating-dominating set if each
vertex of the graph is uniquely distinguished by its distances from the
elements of S, and the minimum cardinality of such a set is called the
metric-location-domination number. In this paper, we undertake a study that, in
general graphs and specific families, relates metric-locating-dominating sets
to other special sets: resolving sets, dominating sets, locating-dominating
sets and doubly resolving sets. We first characterize classes of trees
according to certain relationships between their metric-location-domination
number and their metric dimension and domination number. Then, we show
different methods to transform metric-locating-dominating sets into
locating-dominating sets and doubly resolving sets. Our methods produce new
bounds on the minimum cardinalities of all those sets, some of them involving
parameters that have not been related so far.Comment: 13 pages, 3 figure
