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

David G. L. Wang (), Monica M. Y. Wang () and Shiqiang Zhang ()
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David G. L. Wang: School of Mathematics and Statistics, Beijing Institute of Technology
Monica M. Y. Wang: School of Mathematics and Statistics, Beijing Institute of Technology
Shiqiang Zhang: Department of Computing, Imperial College London

Journal of Combinatorial Optimization, 2022, vol. 43, issue 2, No 9, 460-496

Abstract: 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 $$n\ge 11$$ n ≥ 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.

Keywords: Generalized Petersen graph; Metric dimension; Resolving set; Floyd-Warshall algorithm; 05C30 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00780-8

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