Results 261 to 270 of about 92,183 (289)

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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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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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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On metric dimension of permutation graphs

Journal of Combinatorial Optimization, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael Hallaway, Cong X. Kang, Eunjeong Yi   +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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On the Local Metric Dimension of Graphs

Journal of Interconnection Networks
Let [Formula: see text] be a graph. A set [Formula: see text] is a local resolving set of [Formula: see text] if there exists [Formula: see text] such that [Formula: see text] for any [Formula: see text]. The local metric dimension [Formula: see text] of [Formula: see text] is the minimum cardinality of all the local resolving sets of [Formula: see ...
Chenxu Yang, Xingchao Deng, Jinxia Liang, Yuhu Liu   +3 more
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The metric dimension of amalgamation of cycles

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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Metric dimension and pattern avoidance in graphs

Discrete Applied Mathematics, 2020
Jesse Geneson
exaly