|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|
Show full item record
checked on Oct 2, 2022
checked on Oct 3, 2022
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.