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 graph G, the metric (resp. edge metric) dimension of G is the cardinality
of the smallest ordered set of vertices that uniquely identifies every pair of distinct vertices …

In the aircraft sector, honeycomb composite materials are frequently employed. Recent
research has demonstrated the benefits of honeycomb structures in applications involving …

The edge metric dimension problem was recently introduced, which initiated the study of its
mathematical properties. The theoretical properties of the edge metric representations and …

Graph invariants provide an amazing tool to analyze the abstract structures of graphs. Metric
dimension and edge metric dimension as graph invariants have numerous applications …

Consider an undirected and connected graph G=(VG, EG), where VG and EG represent the
set of vertices and the set of edges respectively. The concept of edge version of metric …

Fault tolerance is the characteristic of a system that permits it to carry on its intended
operations in case of the failure of one of its units. Such a system is known as the fault …

The field of graph theory is extensively used to investigate structure models in biology,
computer programming, chemistry, and combinatorial optimization. In order to work with the …

Metric dimension is a graph parameter motivated by problems in robot navigation, drug
design, and image processing. In this paper, we answer several open extremal problems on …

The number of edges in a shortest walk (without repetition of vertices) from one vertex to
another vertex of a connected graph G is known as the distance between them. For a vertex …