Abstract
Metric dimension is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). Let F be a family of connected graphs Gn: F = (Gn)n≥1 depending on n as follows: the order {pipe}V(G){pipe}=φ(n) and (Formula presented.) If there exists a constant C > 0 such that dim(Gn) ≤C for every n ≥ 1 then we shall say that F has bounded metric dimension. If all graphs in F have the same metric dimension (which does not depend on n), F is called a family with constant metric dimension. In this paper, we study the properties of of some classes of convex polytopes having pendent edges with respect to their metric dimension.
Original language | English |
---|---|
Pages (from-to) | 295-307 |
Number of pages | 13 |
Journal | AKCE International Journal of Graphs and Combinatorics |
Volume | 10 |
Issue number | 3 |
Publication status | Published - Oct 2013 |
Externally published | Yes |
Keywords
- Basis
- Convex polytope
- Metric dimension
- Pendant
- Plane graph
- Resolving set
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics