| Naslov: | On the weak $k$-metric dimension of Hamming graphs |
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| Avtorji: | ID Fernández, Elena (Avtor)
ID Klavžar, Sandi (Avtor)
ID Kuziak, Dorota (Avtor)
ID Muñoz-Márquez, Manuel (Avtor)
ID Yero, Ismael G. (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (967,09 KB)
MD5: B763044489102E3BF1A567EDEFD8DE93
 URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S1572528626000186
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | Given a connected graph $G$, a set of vertices $X\subset V(G)$ is a weak $k$-resolving set of $G$ if for each two vertices $y,z\in V(G)$, the sum of the values $|d_G(y,x)-d_G(z,x)|$ over all $x\in X$ 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 $\mathrm{wdim}_k(G)$. In this paper, $\mathrm{wdim}_k(K_n\,\square\,K_n)$ is determined for every $n\ge 3$ and every $2\le k\le 2n$. An improvement of a known integer linear programming formulation for this problem is developed and implemented for the graphs $K_n\,\square\,K_m$. Conjectures regarding these general situations are posed. |
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| Ključne besede: | weak $k$-metric dimension, weak $k$-resolving set, Cartesian product, Hamming graph |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.05.2026 |
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| Leto izida: | 2026 |
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| Št. strani: | 12 str. |
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| Številčenje: | Vol. 60, article no. 100945 |
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| PID: | 20.500.12556/DiRROS-28314  |
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| UDK: | 519.17:519.8 |
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| ISSN pri članku: | 1572-5286 |
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| DOI: | 10.1016/j.disopt.2026.100945 |
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| COBISS.SI-ID: | 271637763 |
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| Datum objave v DiRROS: | 13.03.2026 |
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| Število ogledov: | 219 |
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| Število prenosov: | 171 |
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| Metapodatki: |    |
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