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

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 …

Due to the immense applications of interconnection networks, various new networks are
designed and extensively used in computer sciences and engineering fields. Networks can …

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

Let G be a connected graph. A vertex w strongly resolves a pair u, v of vertices of G if there
exists some shortest u− w path containing v or some shortest v− w path containing u. A set W …

Minimum resolving sets (edge or vertex) have become an integral part of molecular topology
and combinatorial chemistry. Resolving sets for a specific network provide crucial …

In localization, some specific nodes (beacon set) are selected to locate all nodes of a
network, and if an arbitrary node stops working and still selected nodes remain in the …

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 …

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

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 …