Results 61 to 70 of about 4,232 (158)
The comparative study of resolving parameters for a family of ladder networks
AIMS Mathematics, 2022 For a simple connected graph $ G = (V, E) $, a vertex $ x\in V $ distinguishes two elements (vertices or edges) $ x_1\in V, y_1 \in E $ if $ d(x, x_1)\neq d(x, y_1). $ A subset $ Q_m\subset V $ is a mixed metric generator for $ G, $ if every two distinct
Mohra Zayed +3 more
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Fault-Tolerant Metric Dimension in Carbon Networks
FoundationsIn this paper, we study the fault-tolerant metric dimension in graph theory, an important measure against failures in unique vertex identification. The metric dimension of a graph is the smallest number of vertices required to uniquely identify every ...
Kamran Azhar, Asim Nadeem, Yilun Shang
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On Fault-Tolerant Resolving Sets of Some Families of Ladder Networks
Complexity, 2021 In computer networks, vertices represent hosts or servers, and edges represent as the connecting medium between them. In localization, some special vertices (resolving sets) are selected to locate the position of all vertices in a computer network. If an
Hua Wang +4 more
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DIMENSI METRIK PADA GRAF Rn(q; r)m
Jurnal Matematika UNAND, 2019 The metric dimension of a connected graph G is the cardinality of minimum resolving set in graph G. In this research, how to find the metric dimension of Rn(q; r)m graph. Rn(q; r)m graph is constructing by subdivision operation on Lobster graph Ln(q; r).
Rendy Aditya Pratama +2 more
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On The Local Metric Dimension of Line Graph of Special Graph
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2016 Let G be a simple, nontrivial, and connected graph. is a representation of an ordered set of k distinct vertices in a nontrivial connected graph G. The metric code of a vertex v, where , the ordered of k-vector is representations of v with respect to W,
Marsidi Marsidi +3 more
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Dimension of the Boundary in Different Metrics
MATHEMATICA SCANDINAVICA, 2013 We consider metrics on Euclidean domains $\Omega\subset\mathbf{R}^n$ that are induced by continuous densities $\rho\colon\Omega\rightarrow(0,\infty)$ and study the Hausdorff and packing dimensions of the boundary of $\Omega$ with respect to these metrics.
Ville Suomala, Riku Klén
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On the metric dimension of line graphs
Discrete Applied Mathematics, 2013 Let $G$ be a (di)graph. A set $W$ of vertices in $G$ is a \emph{resolving set} of $G$ if every vertex $u$ of $G$ is uniquely determined by its vector of distances to all the vertices in $W$. The \emph{metric dimension} $ (G)$ of $G$ is the minimum cardinality of all the resolving sets of $G$. C ceres et al. \cite{Ca2} computed the metric dimension of
Min Xu, Min Feng, Kaishun Wang
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The metric dimension of circulant graphs [PDF]
Opuscula MathematicaA pair of vertices \(x\) and \(y\) in a graph \(G\) are said to be resolved by a vertex \(w\) if the distance from \(x\) to \(w\) is not equal to the distance from \(y\) to \(w\).
Tapendra BC, Shonda Dueck
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On the k-metric dimension of metric spaces
Ars Mathematica Contemporanea, 2018 The metric dimension of a general metric space was defined in 1953, applied to the set of vertices of a graph metric in 1975, and developed further for metric spaces in 2013. It was then generalised in 2015 to the k -metric dimension of a graph for each positive integer k , where k = 1 corresponds to the original definition.
Alan F. Beardon +1 more
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DIMENSI METRIK GRAPH LOBSTER Ln (q;r)
E-Jurnal Matematika, 2013 The metric dimension of connected graph G is the cardinality of minimum resolving set in graph G. In this research, we study how to find the metric dimension of lobster graph Ln (q;r).
PANDE GDE DONY GUMILAR +2 more
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