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On the weak k -metric dimension of Hamming graphs

Elena Fernández et al.

Discrete Optimization2026https://doi.org/10.1016/j.disopt.2026.100945article
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0.50

What the paper says

Given a connected graph G , a set of vertices X ⊂ V ( G ) is a weak k -resolving set of G if for each two vertices y , z ∈ V ( G ) , the sum of the values | d G ( y , x ) − d G ( z , x ) | over all x ∈ X is at least k , where d G ( u , v ) stands for the length of a shortest path between u and v . The cardinality of a smallest weak k -resolving set of G is the weak k -metric dimension of G , and is denoted by wdim k ( G ) . In this paper, wdim k ( K n □ K n ) is determined for every n ≥ 3 and every 2 ≤ k ≤ 2 n . An improvement of a known integer linear programming formulation for this problem is developed and implemented for the graphs K n □ K m . Conjectures regarding these general situations are posed.

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https://doi.org/https://doi.org/10.1016/j.disopt.2026.100945

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@article{elena2026,
  title        = {{On the weak k -metric dimension of Hamming graphs}},
  author       = {Elena Fernández et al.},
  journal      = {Discrete Optimization},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1016/j.disopt.2026.100945},
}

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On the weak k -metric dimension of Hamming graphs

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0.50

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F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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