The metric dimension of a graph is a simple way to describe how efficiently one can uniquely identify the position of every vertex in a (di)graph. A resolving set of a (di)graph G is a set of vertices of G such that every vertex in the graph has a unique vector of distances to this set. The metric dimension is the size of a smallest resolving set. In fact, the metric dimension is the minimum number of “landmarks” (vertices from a minimum resolving set) needed so that every vertex in the graph has a unique vector of distances to those landmarks. The study of this characteristic is useful in many applications, such as network navigation and robot localization. In this contribution, we show that the metric dimension of twisted toroidal network \(\overrightarrow{T}_{\!\!m,n}\) is from the set \(\{2, 3, 4, n\}\) .

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On Metric Dimension of Twisted Toroidal Networks Based on Cayley Digraphs

  • Marcel Abas

摘要

The metric dimension of a graph is a simple way to describe how efficiently one can uniquely identify the position of every vertex in a (di)graph. A resolving set of a (di)graph G is a set of vertices of G such that every vertex in the graph has a unique vector of distances to this set. The metric dimension is the size of a smallest resolving set. In fact, the metric dimension is the minimum number of “landmarks” (vertices from a minimum resolving set) needed so that every vertex in the graph has a unique vector of distances to those landmarks. The study of this characteristic is useful in many applications, such as network navigation and robot localization. In this contribution, we show that the metric dimension of twisted toroidal network \(\overrightarrow{T}_{\!\!m,n}\) is from the set \(\{2, 3, 4, n\}\) .