The metric dimension of a graph is the smallest number of nodes required to identify all
other nodes uniquely based on shortest path distances. Applications of metric dimension …

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

Given a connected simple graph G=(V, E) G=(V, E) and a positive integer k, a set S ⊆ VS⊆
V is said to be ak-metric generator for G if and only if for any pair of different vertices u, v ∈ V …

Let G be a connected graph. A vertex w∈ VG/strongly resolves two vertices u, v∈ VG/if
there exists some shortest uw path containing v or some shortest vw path containing u. A set …

A vertex v ∈ V (G) v∈ V (G) is said to distinguish two vertices x, y ∈ V (G) x, y∈ V (G) of a
nontrivial connected graph G if the distance from v to x is different from the distance from v to …

A metric generator is a set W of vertices of a graph G (V, E) such that for every pair of vertices
u, v of G, there exists a vertex w∈ W with the condition that the length of a shortest path from …

Let G be a connected graph. Given an ordered set W={w 1,..., wk}⊆ V (G) and a vertex u∈ V
(G), the representation of u with respect to W is the ordered k-tuple (d (u, w 1), d (u, w 2),..., d …

The concept of resolving the set within a graph is related to the optimal placement problem
of access points in an indoor positioning system. A vertex w of the undirected connected …

A subset S of vertices is a resolving set in a graph if every vertex has a unique array of
distances to the vertices of S. Consequently, we can locate any vertex of the graph with the …

Given a connected graph G, a vertex w ∈ V (G) w∈ V (G) distinguishes two different vertices
u, v of G if the distances between w and u, and between w and v are different. Moreover, w …