Abstract Let G=(V, E) be a connected graph. A vertex w∈ V distinguishes two elements
(vertices or edges) x, y∈ E∪ V if d G (w, x)≠ d G (w, y). A set S of vertices in a connected …

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

An edge metric generator of a connected graph G is a vertex subset S for which every two
distinct edges of G have distinct distance to some vertex of S, where the distance between a …

Let Γ=(V, E) be a connected graph. A vertex i∈ V recognizes two elements (vertices or
edges) j, k∈ E∩ V, if d Γ (i, j)≠ d Γ (i, k). A set S of vertices in a connected graph Γ is a …

Abstract If S={v_1, ..., v_k\} S= v 1,…, vk is an ordered subset of vertices of a connected
graph G and e is an edge of G, then the vector r_G (e| S)=(d_G (v_1, e), ..., d_G (v_k, e)) r G …

Let G=(V, E) be a simple connected graph, w∈ V be a vertex, and e= uv∈ E be an edge.
The distance between the vertex w and edge e is given by d (e, w)= min {d (w, u), d (w, v)}, A …

A molecular (chemical) graph is a simple connected graph, where the vertices represent the
compound's atoms and the edges represent bonds between the atoms, and the degree …

The concept of a metric dimension was proposed to model robot navigation where the
places of navigating agents can change among nodes. The metric dimension md (G) of a …

Social network data is typically made available in a graph format, where users and their
relations are represented by vertices and edges, respectively. In doing so, social graphs …

The partition dimension problem is to decompose the vertex set of a graph into minimum
number of vertex disjoint sets such that the ordered distances between every vertex of the …