Results 211 to 220 of about 1,385,922 (245)

THE METRIC DIMENSION OF METRIC MANIFOLDS

Bulletin of the Australian Mathematical Society, 2015
In this paper we determine the metric dimension of $n$-dimensional metric $(X,G)$-manifolds. This category includes all Euclidean, hyperbolic and spherical manifolds as special cases.
Heydarpour, Majid, Maghsoudi, Saeid
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The Metric Dimension of Metric Spaces

Computational Methods and Function Theory, 2013
Let \((X,d)\) be a metric space. A non-empty subset \(A\) of \(X\) resolves \((X,d)\) if \(d(x,a)=d(y,a)\) for all \(a\) in \(A\) implies \(x=y\), and if that is so we may regard the distances \(d(x,a)\), where \(a\in A\), as the coordinates of \(x\) with respect to \(A\).
Bau, Sheng, Beardon, Alan F.
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On the Metric Dimension of Certain Metric Manifolds

Bulletin of the Iranian Mathematical Society, 2020
Recall that the metric dimension, \(\mathrm{md}(X)\) of a metric space \((X,d)\) is the minimal cardinality of a resolving set, i.e. a non-empty set \(A\subset X\) such that for any \(x,y\in X\), if \(d(x,a)=d(y,a)\) for all \(a\in X\) then \(x=y\).
Heydarpour, Majid, Maghsoudi, Saeid
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Edge metric dimension and mixed metric dimension of a plane graph Tn

Discrete Mathematics, Algorithms and Applications, 2023
Let [Formula: see text] be a connected graph where [Formula: see text] is the set of vertices of [Formula: see text] and [Formula: see text] is the set of edges of [Formula: see text]. The distance from the vertex [Formula: see text] to the edge [Formula: see text] is given by [Formula: see text].
Huige Shen, Jing Qu, Na Kang, Cong Lin
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The k-metric dimension

Journal of Combinatorial Optimization, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ron Adar, Leah Epstein
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Mixed Metric Dimension of Graphs [PDF]

Applied Mathematics and Computation, 2017
arXiv admin note: text overlap with arXiv:1602 ...
Dorota Kuziak, Ismael Gonzalez Yero, Andrej Taranenko   +2 more
exaly   +5 more sources

On {ℓ}-Metric Dimensions in Graphs

Fundamenta Informaticae, 2018
A subset S of vertices is a resolving set in a graph if every vertex has a unique array of distances to the vertices of S. Consequently, we can locate any vertex of the graph with the aid of the distance arrays. The problem of finding the smallest cardinality of a resolving set in a graph has been widely studied over the years.
Anni Hakanen, Tero Laihonen
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ON FRACTIONAL METRIC DIMENSION OF GRAPHS

Discrete Mathematics, Algorithms and Applications, 2013
A vertex x in a connected graph G = (V, E) is said to resolve a pair {u, v} of vertices of G if the distance from u to x is not equal to the distance from v to x. The resolving neighborhood for the pair {u, v} is defined as R{u, v} = {x ∈ V : d(u, x) ≠ d(v, x)}.
S. Arumugam 0001, Varughese Mathew, Jian Shen   +2 more
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Dimension and metric

Chaos, Solitons & Fractals, 2002
Abstract We briefly discuss the nature of space, its metric and dimension in the spirit of El Naschie's Cantorian space-time.
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Ulam’s Metric in Higher Dimensions

Ulam’s metric defines the minimal number of moves (extrac-tion followed by re-insertion of permutation elements) to go between a given pair of permutations, and determination of moved elements resolves the Longest Common Subsequence problem. The extensive research that followed Ulam’s work provided many influential discoveries in computer science ...
Sebastian Bala, Andrzej Kozik
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