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 …

Abstract Let G=(V, E) G=(V, E) be a connected graph. Given a vertex v ∈ V v∈ V and an
edge e= uw ∈ E e= uw∈ E, the distance between v and e is defined as d_G (e, v)=\min …

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

A set of vertices W is a resolving set of a graph G if every two vertices of G have distinct
representations of distances with respect to the set W. The number of vertices in a smallest …

Let Γ be a simple connected undirected graph with vertex set V (Γ) and edge set E (Γ). The
metric dimension of a graph Γ is the least number of vertices in a set with the property that …

The metric dimension is quite a well-studied graph parameter. Recently, the adjacency
metric dimension and the local metric dimension have been introduced. We combine these …

The metric dimension of a graph G is the smallest size of a set R of vertices that can
distinguish each vertex pair of G by the shortest-path distance to some vertex in R …

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 …

A set of vertices W resolves a graph G if every vertex of G is uniquely determined by its
vector of distances to the vertices in W. The metric dimension for G, denoted by dim (G), is …

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