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The dominant metric dimension of graphs [PDF]
Heliyon, 2020 The G be a connected graph with vertex set V(G) and edge set E(G). A subset S⊆V(G) is called a dominating set of G if for every vertex x in V(G)∖S, there exists at least one vertex u in S such that x is adjacent to u.
Liliek Susilowati +4 more
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Metric dimension and edge metric dimension of windmill graphs
AIMS Mathematics, 2021 Graph invariants provide an amazing tool to analyze the abstract structures of graphs. Metric dimension and edge metric dimension as graph invariants have numerous applications, among them are robot navigation, pharmaceutical chemistry, etc.
Pradeep Singh +3 more
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On Metric Dimension of Functigraphs [PDF]
Discrete Mathematics, Algorithms and Applications, 2012 The \emph{metric dimension} of a graph $G$, denoted by $\dim(G)$, is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices.
Bailey R. F. +17 more
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On the metric dimension and fractional metric dimension for hierarchical product of graphs [PDF]
Applicable Analysis and Discrete Mathematics, 2012 A set of vertices $W$ {\em resolves} a graph $G$ if every vertex of $G$ is uniquely determined by its vector of distances to the vertices in $W$. The {\em metric dimension} for $G$, denoted by $\dim(G)$, is the minimum cardinality of a resolving set of ...
Feng, Min, Wang, Kaishun
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The Metric Dimension and Local Metric Dimension of Relative Prime Graph [PDF]
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2020 This study aims to determine the value of metric dimensions and local metric dimensions of relative prime graphs formed from modulo integer rings, namely . As a vertex set is and if and are relatively prime.
Inna Kuswandari +2 more
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Metric and fault-tolerant metric dimension for GeSbTe superlattice chemical structure [PDF]
PLoS ONE, 2023 The concept of metric dimension has many applications, including optimizing sensor placement in networks and identifying influential persons in social networks, which aids in effective resource allocation and focused interventions; finding the source of ...
Liu Liqin +4 more
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Metric dimension for random graphs [PDF]
The Electronic Journal of Combinatorics, 2013 The metric dimension of a graph $G$ is the minimum number of vertices in a subset $S$ of the vertex set of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $S$.
Bollobas, B., Mitsche, D., Pralat, P.
core +7 more sources
Computing the Mixed Metric Dimension of a Generalized Petersen Graph P(n, 2)
Frontiers in Physics, 2020 Let Γ = (V, E) be a connected graph. A vertex i ∈ V recognizes two elements (vertices or edges) j, k ∈ E ∩ V, if dΓ(i, j) ≠ dΓ(i, k). A set S of vertices in a connected graph Γ is a mixed metric generator for Γ if every two distinct elements (vertices or
Hassan Raza
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Metric characterizations of dimension for separable metric spaces [PDF]
Proceedings of the American Mathematical Society, 1978 A subset B of a metric space (X, d) is called a d-bisector set iff there are distinct points x and y in X with B = { z : d ( x , z ) = d ( y , z ) } B = \{ z:d(x,z) = d(y,z)\} .
Ludvík Janoš, Harold W. Martin
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On the k-metric Dimension of Metric Spaces [PDF]
arXiv, 2016 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.
Beardon, A. F. +1 more
arxiv +3 more sources