Computing the metric dimension of kayak paddles graph and cycles with chord

Abstract

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 resolving set is called the metric dimension. This invariant has extensive applications in robotics, since the metric dimension can represent the mínimum number of landmarks, which uniquely determine the position of a robot moving in a graph space. Finding the metric dimension of a graph is an NP-hard problem. We present exact values of the metric dimensión of Kayak Paddles graph and Cycles with chord.

Topics & Concepts