|
|
 |
| |
|
|
|
Metric Dimension and Exchange Property for Resolving Sets in Rotationally-Symmetric Graphs |
|
|
|
PP: 1665-1674 |
|
|
|
Author(s) |
|
|
|
Rishi Naeem,
Muhammad Imran,
|
|
|
|
Abstract |
|
|
| Metric dimension or location number 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 |V(G)| = j(n) and
lim
n→¥
j(n) = ¥. 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, otherwise F has unbounded 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 metric dimension of quasi flower snarks, generalized antiprism and cartesian product of square cycle
and path. We prove that these classes of graphs have constant or bounded metric dimension. It is natural to ask for characterization of
graphs classes with respect to the nature of their metric dimension. It is also shown that the exchange property of the bases in a vector
space does not hold for minimal resolving sets of quasi flower snarks, generalized prism and generalized antiprism. |
|
|
|
|
|
|
|
