On the metric dimension of convex polytopes

Muhammad Imran; Syed Ahtsham Ul Haq Bokhary; A. Q. Baig

On the metric dimension of convex polytopes

Muhammad Imran, Syed Ahtsham Ul Haq Bokhary, A. Q. Baig

Research output: Contribution to journal › Article › peer-review

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 G_n: F = (G_n)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(G_n) ≤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

Cite this

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On the metric dimension of convex polytopes

Abstract

Keywords

ASJC Scopus subject areas

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