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Notions of Metric Dimension of Corona Products: Combinatorial and Computational Results

  • Henning Fernau
  • Juan Alberto Rodríguez-Velázquez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8476)

Abstract

The metric dimension is quite a well-studied graph parameter. Recently, the adjacency metric dimension and the local metric dimension have been introduced. We combine these variants and introduce the local adjacency metric dimension. We show that the (local) metric dimension of the corona product of a graph of order n and some non-trivial graph H equals n times the (local) adjacency metric dimension of H. This strong relation also enables us to infer computational hardness results for computing the (local) metric dimension, based on according hardness results for (local) adjacency metric dimension that we also give.

Keywords

(local) metric dimension (local) adjacency dimension NP-hardness 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Henning Fernau
    • 1
  • Juan Alberto Rodríguez-Velázquez
    • 2
  1. 1.FB 4-Abteilung InformatikwissenschaftenUniversität TrierTrierGermany
  2. 2.Universitat Rovira i VirgiliTarragonaSpain

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