Authors: Kratica, Jozef 
Kovačević-Vujčić, Vera
Čangalović, Mirjana
Stojanović, Milica
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Minimal doubly resolving sets and the strong metric dimension of hamming graphs
Journal: Applicable Analysis and Discrete Mathematics
Volume: 6
Issue: 1
First page: 63
Last page: 71
Issue Date: 1-Apr-2012
Rank: M21
ISSN: 1452-8630
DOI: 10.2298/AADM111116023K
Abstract: 
We consider the problem of determining the cardinality ψ (H 2,k) of minimal doubly resolving sets of Hamming graphs H 2,k.We prove that for k ≥ 6 every minimal resolving set of H 2,k is also a doubly resolving set, and, consequently, ψ (H 2,k) is equal to the metric dimension of H 2,k, which is known from the literature. Moreover, we find an explicit expression for the strong metric dimension of all Hamming graphs H n,k.
Keywords: Graph theory | Hamming graphs | Metric dimension | Minimal doubly resolving set | Strong metric dimension
Publisher: School of Electric Engineering, University of Belgrade

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