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Metric Mean Dimension via Preimage Structures
Journal of Statistical PhysicsLet \((X, d)\) be a compact metric space and \(f : X\to X\) be a continuous map. \textit{M. Hurley} [Ergodic Theory Dyn. Syst. 15, No. 3, 557--568 (1995; Zbl 0833.54021)] introduced the topological preimage entropy of \(f\) as follows \[ h_m(f)=\lim_{\varepsilon \rightarrow 0} h_m(f,\varepsilon ) =\underset{n\rightarrow \infty }{\lim \sup }\frac{1}{n ...
Chunlin Liu, Fagner B. Rodrigues
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Metric dimensions of metric spaces over integers
Quaestiones Mathematicae, 2019We consider metric spaces over the ring of integers. For any generating set S of ℤ, it is shown that the metric dimension of the metric space X = X(ℤ, S) is not greater than 2 max S.
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Getting the Lay of the Land in Discrete Space: A Survey of Metric Dimension and Its Applications
SIAM Review, 2023Rafael M Frongillo, Manuel E Lladser
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Metric dimension and pattern avoidance in graphs
Discrete Applied Mathematics, 2020Jesse Geneson
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Uniquely identifying the edges of a graph: The edge metric dimension
Discrete Applied Mathematics, 2018Niko Tratnik, Ismael G Yero
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Resolvability in graphs and the metric dimension of a graph
Discrete Applied Mathematics, 2000Ortrud R Oellermann
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On the Metric Dimension of Cartesian Products of Graphs
SIAM Journal on Discrete Mathematics, 2007José Cáceres +2 more
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On the fault-tolerant metric dimension of certain interconnection networks
Journal of Applied Mathematics and Computing, 2018Hassan Raza +2 more
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