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The metric dimension of amalgamation of cycles [PDF]

, 2010
Summary: For an ordered set \(W = \{w_1, w_2, \dots, w_k\}\) of vertices and a vertex \(v\) in a connected graph \(G\), the representation of \(v\) with respect to \(W\) is the ordered \(k\)-tuple \(r(v|W) = (d(v,w_1), d(v,w_2), \dots, d(v,w_k))\) where \(d(x,y)\) represents the distance between the vertices \(x\) and \(y\).
Iswadi, Hazrul, Baskoro, Edy Tri, Salman, A.N.M, Simanjuntak, Rinovia   +3 more
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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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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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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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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].
Shen, Huige, Qu, Jing, Kang, Na, Lin, Cong   +3 more
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The k-metric dimension

Journal of Combinatorial Optimization, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Adar, Ron, Epstein, Leah
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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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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.
Hakanen Anni, Laihonen Tero
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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)}.
Arumugam, S., Mathew, Varughese, Shen, Jian   +2 more
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