Topics concerning metric dimension related invariants in graphs are nowadays intensively
studied. This compendium of combinatorial and computational results on this topic is an …

The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum
number of landmark nodes needed to distinguish every pair of nodes in the graph based on …

Let G=(V, E) be a finite simple connected graph. We say a graph G realizes a code of the
type 0^ s_1 1^ t_1 0^ s_2 1^ t_2... 0^ s_k1^ t_k if and only if G can obtained from the code by …

Let G be a connected graph and u, v and w vertices of G. Then w is said to strongly resolve u
and v, if there is either a shortest uw path that contains v or a shortest vw path that contains …

We investigate how the metric dimension of infinite graphs change when we add edges to
the graph. Our two main results:(1) there exists a growing sequence of graphs (under the …

Let G be a connected graph and u, v and w vertices of G. Then w is said to resolve u and v if
the distance from u to w does not equal the distance from v to w. If there is either a shortest …

Let $ G $ be a graph, and let $ u $, $ v $, and $ w $ be vertices of $ G $. If the distance
between $ u $ and $ w $ does not equal the distance between $ v $ and $ w $, then $ w $ is …