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Vertex and Edge Dimension of Hypergraphs

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Abstract

Let G = (V, E) be a connected graph and let \({W = (w_{1}, \ldots,w_{k})}\) be an ordered subset of V. The k-vector \({r(v|W) = (d(v, w_{1}), \ldots, d(v, w_{k}))}\) is called the metric representation of v with respect to W. The set W is a resolving set of G if r(u|W) = r(v|W) implies u = v. The minimum cardinality of a resolving set in G is the metric dimension of G. In this paper we extend the notion of metric dimension to hypergraphs. We also introduce the dual concept, that is, edge dimension for hypergraphs, and initiate a study on this parameter.

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Authors and Affiliations

  1. National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, Krishnankoil, 626 126, India

    Martín Manrique & S. Arumugam

  2. School of Electrical Engineering and Computer Science, The University of Newcastle, Newcastle, NSW, 2308, Australia

    S. Arumugam

  3. Department of Computer Science, Liverpool Hope University, Liverpool, UK

    S. Arumugam

  4. Department of Computer Science, Ball State University, Muncie, USA

    S. Arumugam

Authors
  1. Martín Manrique
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  2. S. Arumugam
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Correspondence to S. Arumugam.

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Manrique, M., Arumugam, S. Vertex and Edge Dimension of Hypergraphs. Graphs and Combinatorics 31, 183–200 (2015). https://doi.org/10.1007/s00373-013-1384-y

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  • DOI: https://doi.org/10.1007/s00373-013-1384-y

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