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## On the metric dimension of rotationally-symmetric convex polytopes

#### Muhammad Imran [1] , Syed Ahtsham Ul Haq Bokhary [2] , A. Q. Baig [3]

Metric dimension is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). Let $\mathcal{F}$ be a family of connected graphs $G_{n}$ : $\mathcal{F} = (G_{n})_{n}\geq 1$ depending on $n$ as follows: the order $|V(G)| = \varphi(n)$ and $\lim\limits_{n\rightarrow \infty}\varphi(n)=\infty$. If there exists a constant $C > 0$ such that $dim(G_{n}) \leq C$ for every $n \geq 1$ then we shall say that $\mathcal{F}$ has bounded metric dimension, otherwise $\mathcal{F}$ has unbounded metric dimension. If all graphs in $\mathcal{F}$ have the same metric dimension, then $\mathcal{F}$ is called a family of graphs with constant metric dimension.

In this paper, we study the metric dimension of some classes of convex polytopes which are rotationally-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 these classes of convex polytopes. It is natural to ask for the characterization of classes of convex polytopes with constant metric dimension.

Metric dimension, Basis, Resolving set, Prism, Antiprism, Convex polytopes
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Subjects Engineering Articles Author: Muhammad Imran Author: Syed Ahtsham Ul Haq Bokhary Author: A. Q. Baig Publication Date : May 15, 2016
 Bibtex @research article { jacodesmath285342, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2016}, volume = {3}, pages = {45 - 59}, doi = {10.13069/jacodesmath.47485}, title = {On the metric dimension of rotationally-symmetric convex polytopes}, key = {cite}, author = {Imran, Muhammad and Bokhary, Syed Ahtsham Ul Haq and Baig, A. Q.} } APA Imran, M , Bokhary, S , Baig, A . (2016). On the metric dimension of rotationally-symmetric convex polytopes . Journal of Algebra Combinatorics Discrete Structures and Applications , 3 (2) , 45-59 . DOI: 10.13069/jacodesmath.47485 MLA Imran, M , Bokhary, S , Baig, A . "On the metric dimension of rotationally-symmetric convex polytopes" . Journal of Algebra Combinatorics Discrete Structures and Applications 3 (2016 ): 45-59 Chicago Imran, M , Bokhary, S , Baig, A . "On the metric dimension of rotationally-symmetric convex polytopes". Journal of Algebra Combinatorics Discrete Structures and Applications 3 (2016 ): 45-59 RIS TY - JOUR T1 - On the metric dimension of rotationally-symmetric convex polytopes AU - Muhammad Imran , Syed Ahtsham Ul Haq Bokhary , A. Q. Baig Y1 - 2016 PY - 2016 N1 - doi: 10.13069/jacodesmath.47485 DO - 10.13069/jacodesmath.47485 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 45 EP - 59 VL - 3 IS - 2 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.47485 UR - https://doi.org/10.13069/jacodesmath.47485 Y2 - 2020 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications On the metric dimension of rotationally-symmetric convex polytopes %A Muhammad Imran , Syed Ahtsham Ul Haq Bokhary , A. Q. Baig %T On the metric dimension of rotationally-symmetric convex polytopes %D 2016 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 3 %N 2 %R doi: 10.13069/jacodesmath.47485 %U 10.13069/jacodesmath.47485 ISNAD Imran, Muhammad , Bokhary, Syed Ahtsham Ul Haq , Baig, A. Q. . "On the metric dimension of rotationally-symmetric convex polytopes". Journal of Algebra Combinatorics Discrete Structures and Applications 3 / 2 (May 2016): 45-59 . https://doi.org/10.13069/jacodesmath.47485 AMA Imran M , Bokhary S , Baig A . On the metric dimension of rotationally-symmetric convex polytopes. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016; 3(2): 45-59. Vancouver Imran M , Bokhary S , Baig A . On the metric dimension of rotationally-symmetric convex polytopes. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016; 3(2): 45-59.