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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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
- Generalized Petersen graph
- Metric dimension
- Resolving set
- Floyd-Warshall algorithm
Mathematics Subject Classification