Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 63-67 |
Number of pages | 5 |
Journal | Applied Mathematics and Information Sciences |
Volume | 9 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2015 |
Externally published | Yes |
Keywords
- Diameter
- Exchange property
- Metric dimension
- Necklace graph
- R-set
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics