Abstract
Let W = (w1, w2, .... wk) be an ordered set of vertices of G and let ν be a vertex of G. The representation r(ν|W) of ν with respect to W is the k-tuple (d(ν, w1), d(ν, w2), ..., d(ν, wk)). W is called a resolving set or a locating set if every vertex of G is uniquely identified by its distances from the vertices of W , or equivalently, if distinct vertices of G have distinct representations with respect to W . A resolving set of minimum cardinality is called a metric basis for G and this cardinality is the metric dimension of G, denoted by dim (G). Metric dimension is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). In this paper, we study the metric dimension of barycentric subdivision of Cayley graphs Cay(Zn⊕Zm). We prove that these subdivisions of Cayley graphs have constant metric dimension and only three vertices chosen appropriately suffice to resolve all the vertices of Cayley graphs Cay(Zn⊕Zm).
Original language | English |
---|---|
Pages (from-to) | 637-646 |
Number of pages | 10 |
Journal | Miskolc Mathematical Notes |
Volume | 16 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2015 |
Externally published | Yes |
Keywords
- Barycentric subdivision
- Basis
- Cayley graph
- Metric dimension
- Resolving set
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Numerical Analysis
- Discrete Mathematics and Combinatorics
- Control and Optimization