The p-type networks are designed with the help of CVNET at topo group Cluj and also given
support by nano studio. Such networks develop new p-type surfaces and also represent the …

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 …

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 …

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

Let be a connected graph and for a given-ordered partition of vertices of a connected graph
is represented as. The representation of a vertex is the vector. The partition is a resolving …

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 …

Abstract Let G=(V (G), E (G)) be a connected graph and d (f, y) denotes the distance
between edge f and vertex y, which is defined as d (f, y)= min {d (p, y), d (q, y)}, where f= pq …

A vertex u∈ V (G) resolves (distinguish or recognize) two elements (vertices or edges) v,
w∈ E (G) UV (G) if d G (u, v)≠ d G (u, w). A subset L m of vertices in a connected graph G is …

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 …

In this paper we consider two similar optimization problems on graphs: the strong metric
dimension problem and the problem of determining minimal doubly resolving sets. We prove …