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 …

In network theory, distance parameters are crucial in analyzing structural aspects of the
networks under investigation, including their symmetry, connectedness, and tendency to …

Let G be a graph with vertex set V (G) and edge set E (G). For any e∈ E (G) and u, v∈ V (G),
the edge e is monitored by two vertices u and v in graph G if d G (u, v)≠ d G− e (u, v). A set …

A set of vertices S⊆ V (G) is a resolving set of a graph G if for each x, y∈ V (G) there is a
vertex u∈ S such that d (x, u)≠ d (y, u). A resolving set S is a fault-tolerant resolving set if …

The doubly metric dimension of a connected graph G is the minimum cardinality of doubly
resolving sets in it. It is well known that deciding the doubly metric dimension of G is NP …

Nonlocal metric dimension dim n ℓ (G) of a graph G is introduced as the cardinality of a
smallest nonlocal resolving set, that is, a set of vertices which resolves each pair of non …

In a graph G, a vertex (resp. an edge) metric generator is a set of vertices S such that any
pair of vertices (resp. edges) from G is distinguished by at least one vertex from S. The …

This work focuses on the (k, ℓ)-anonymity of some networks as a measure of their privacy
against active attacks. Two different types of networks are considered. The first one consists …

The understanding of the structure of a network can be enhanced efficiently with distance-
reliant parameters. The metric dimension is one such parameter with numerous variations …

Two vertices u, v in a connected graph G are doubly resolved by x, y∈ G if d (v, x)− d (u, x)≠
d (v, y)− d (u, y). A set W of vertices of the graph G is a doubly resolving set for G if every two …