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

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(nk) 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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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 (2021). https://doi.org/10.1007/s10878-021-00780-8

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Keywords

  • Generalized Petersen graph
  • Metric dimension
  • Resolving set
  • Floyd-Warshall algorithm

Mathematics Subject Classification

  • 05C30