On metric dimension of flower graphs fnχm and convex polytopes
Loading...
Date
2013
Journal Title
Journal ISSN
Volume Title
Publisher
Utilitas Mathematica
Abstract
Let G be a connected graph and d(x, y) be the dis-tance between the vertices x and y. A subset of vertices W ={w1,w2, · · · ,wk} is called a resolving set for G if for every two
distinct vertices x, y ∈ V (G), there is a vertex wi ∈ W such that
d(x,wi) 6= d(y,wi). A resolving set containing a minimum number
of vertices is called a metric basis for G and the number of vertices
in a metric basis is its metric dimension dim(G).
Let F be a family of connected graphs Gn : F = (Gn)n 1 depend-
ing on n as follows: the order |V (G)| = '(n) and lim
n!1
'(n) = ∞.
If there exists a constant C > 0 such that dim(G) ≤ 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),
then F is called a family with constant metric dimension.
The metric dimension of some classes of plane graphs has been de-
termined in [3], [4], [5], [10], [12], [15] and [22], while metric dimen-
sion of some classes of convex polytopes has been studied in [10].
In this paper this study is extended, by considering flower graphs
fn×m and two classes of graphs associated to convex polytopes.
Description
Keywords
Metric Dimension, Basis, Resolving set, Convex polytopes, Flower graphs
Citation
Imran, M., Bashir, F., Baig, A. Q., Ul, S. A., Bokhary, H., Riasat, A., & Tomescu, I. (2013). On metric dimension of flower graphs fnχm and convex polytopes. Utilitas Mathematica, 289-409.