In this paper we introduce generalized Möbius ladder Mm,n and give its metric dimension. Moreover, it is observed that, depending on even and odd values of m and n, it has two subfamilies with constant metric dimensions.

In a graph G = (V, E), a vertex v ∈ V is said to distinguish two vertices x and y if dG(v, x) 6= dG(v, y). A set S ⊆ V is said to be a local metric generator for G if any pair of adjacent vertices of G is distinguished by some element of S. A minimum local metric generator is called a local metric basis and its cardinality the local metric dimension of G. A set S ⊆ V is said to be a simultaneou...

A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of a graph G is the minimum cardinality of a resolving set. In this paper we study the metric dimension of infinite graphs such that all its vertices have finite degree. We give necessary conditions for those graphs to have finite metric dimension a...

Generation of realistic topologies plays an important role in determining the accuracy and validity of simulation studies. This study presents a discussion to justify why, and how often randomly generated adjacency matrices may not not conform to wireless topologies in the physical world. Specifically, it shows through analysis and random trials that, more than 90% of times, a randomly generate...