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 …

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 …

Polyphenyl is used in a variety of applications including high‐vacuum devices, optics, and
electronics, and in high‐temperature and radiation‐resistant fluids and greases, it has low …

A set of vertices W is a resolving set of a graph G if every two vertices of G have distinct
representations of distances with respect to the set W. The number of vertices in a smallest …

A set of vertices W resolves a graph G if every vertex is uniquely determined by its
coordinate of distance to the vertices in W. The minimum cardinality of a resolving set of G is …

For a connected graph G=(V, E), an ordered set R={r 1, r 2,…, rk}⊂ V (G) is said to be a
resolving set if c (u| R)≠ c (v| R) for every distinct pair of vertices u, v of G, where c (w| R)=(d …

Abstract Let G=(V, E) be a connected graph and d (x, y) be the distance between the vertices
x and y in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by …

Concepts of resolving set and metric basis has enjoyed a lot of success because of multi-
purpose applications both in computer and mathematical sciences. For a connected graph G …

In this paper, we study the metric dimension of barycentric subdivision of Möbius ladders
and the metric dimension of generalized Petersen multigraphs. We prove that the …

Let Γ be a simple connected undirected graph with vertex set V (Γ) and edge set E (Γ). The
metric dimension of a graph Γ is the least number of vertices in a set with the property that …