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Determining the edge metric dimension of the generalized Petersen graph P(n, 3)

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Abstract

It is known that the problem of computing the edge dimension of a graph is NP-hard, and that the edge dimension of any generalized Petersen graph P(n, k) is at least 3. We prove that the graph P(n, 3) has edge dimension 4 for \(n\ge 11\), by showing semi-combinatorially the nonexistence of an edge resolving set of order 3 and by constructing explicitly an edge resolving set of order 4.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, 102400, Beijing, People’s Republic of China

    David G. L. Wang & Monica M. Y. Wang

  2. Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, 102400, Beijing, People’s Republic of China

    David G. L. Wang

  3. Key Laboratory of Mathematical Theory and Computation in Information Security, Ministry of Industry and Information Technology, 102400, Beijing, People’s Republic of China

    David G. L. Wang

  4. Department of Computing, Imperial College London, SW7 2AZ, London, United Kingdom

    Shiqiang Zhang

Authors
  1. David G. L. Wang
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  2. Monica M. Y. Wang
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  3. Shiqiang Zhang
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Correspondence to David G. L. Wang.

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This paper was supported by National Natural Science Foundation of China (Grant No. 11671037)

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Wang, D.G.L., Wang, M.M.Y. & Zhang, S. Determining the edge metric dimension of the generalized Petersen graph P(n, 3). J Comb Optim 43, 460–496 (2022). https://doi.org/10.1007/s10878-021-00780-8

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  • DOI: https://doi.org/10.1007/s10878-021-00780-8

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