A convex polytopes is a polytope that is also a convex set of points in the n-dimensional
Euclidean space R n. By preserving the same adjacency relation between vertices of a …

The position of a moving point in a connected graph can be identified by computing the
distance from the point to a set of sonar stations which have been appropriately situated in …

A fixed interconnection parallel architecture is characterized by a graph, with vertices
corresponding to processing nodes and edges representing communication links. An …

Metric dimension and fault-tolerant metric dimension have potential applications in
telecommunication, robot navigation and geographical routing protocols, among others. The …

In this paper, we study resolvability and fault-tolerant resolvability of convex polytopes and
related geometric graphs. Imran et al.(2010)[18] raised an open problem asserting that …

In this paper, we consider fault-tolerant resolving sets in graphs. We characterize n-vertex
graphs with fault-tolerant metric dimension n, n− 1, and 2, which are the lower and upper …

A motion of a robot in space is represented by a graph. A robot change its position from point
to point and its position can be determined itself by distinct labelled landmarks points. The …

We characterize the strong metric dimension of the power graph of a finite group. As
applications, we compute the strong metric dimension of the power graph of a cyclic group …

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 …

An ordered set W={w 1,…, wk}⊆ V (G) of vertices of G is called a resolving set or locating set
for G if every vertex is uniquely determined by its vector of distances to the vertices in W. A …