The R-set relative to a pair of distinct vertices of a connected graph G is the set of vertices whose distances to these vertices are distinct. In this paper R-sets are used to show that metric dimension dim(Nen) = 3 when n is odd and 2 otherwise, where Nen is the necklace graph of order 2n+2. It is also shown that the exchange property of the bases in a vector space does not hold for minimal resolving sets of Nen if n is even.
Digital Object Identifier (DOI)
Tomescu, Ioan and Imran, Muhammad
"R-Sets and Metric Dimension of Necklace Graphs,"
Applied Mathematics & Information Sciences: Vol. 09:
1, Article 16.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss1/16