On the metric dimension of rotationally-symmetric convex polytopes

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Muhammad Imran¹  Syed Ahtsham Ul Haq Bokhary²  A. Q. Baig³ 

[1] Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST);Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University;Department of Mathematics, COMSATS Institute of Information Technology

关键词: Metric dimension;    Basis;    Resolving set;    Prism;    Antiprism;    Convex polytopes;   

DOI  :  10.13069/jacodesmath.47485

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

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 asfollows: the order |V (G)| = ϕ(n) and limn→∞ϕ(n) = ∞. If there exists a constant C > 0 such thatdim(Gn) ≤ C for every n ≥ 1 then we shall say that F has bounded metric dimension, otherwiseF has unbounded metric dimension. If all graphs in F have the same metric dimension, then F iscalled a family of graphs with constant metric dimension.In this paper, we study the metric dimension of some classes of convex polytopes which arerotationally-symmetric. It is shown that these classes of convex polytoes have the constant metric dimension and only three vertices chosen appropriately suffice to resolve all the vertices of theseclasses of convex polytopes. It is natural to ask for the characterization of classes of convex polytopeswith constant metric dimension.

【 授权许可】

CC BY