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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.
Beardon, Alan F. +1 more
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Intrinsic Dimension Estimation for Discrete Metrics
Physical Review Letters, 2023 Real world-datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods are designed for continuous spaces, and their use for discrete spaces can lead to errors and biases.
Macocco, Iuri +3 more
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Computing dominant metric dimensions of certain connected networks
HeliyonIn the studies of the connected networks, metric dimension being a distance-based parameter got much more attention of the researches due to its wide range of applications in different areas of chemistry and computer science. At present its various types
Imtiaz Ali, Muhammad Javaid, Yilun Shang
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The Dominant Metric Dimension of Corona Product Graphs
مجلة بغداد للعلوم, 2021 The metric dimension and dominating set are the concept of graph theory that can be developed in terms of the concept and its application in graph operations.
Rembulan Putri Adirasari +2 more
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The Simultaneous Metric Dimension of Families Composed by Lexicographic Product Graphs
, 2015 Let ${\mathcal G}$ be a graph family defined on a common (labeled) vertex set $V$. A set $S\subseteq V$ is said to be a simultaneous metric generator for ${\cal G}$ if for every $G\in {\cal G}$ and every pair of different vertices $u,v\in V$ there exists
Estrada-Moreno, Alejandro +2 more
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IEEE AccessIn the aircraft sector, honeycomb composite materials are frequently employed. Recent research has demonstrated the benefits of honeycomb structures in applications involving nanohole arrays in anodized alumina, micro-porous arrays in polymer thin films,
Sidra Bukhari +3 more
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On Adjacency Metric Dimension of Some Families of Graph
Journal of Function Spaces, 2022 Metric dimension of a graph is a well-studied concept. Recently, adjacency metric dimension of graph has been introduced. A set Qa⊂VG is considered to be an adjacency metric generator for G if u1,u2∈V\Qa (supposing each pair); there must exist a vertex q∈
Ali N. A. Koam +4 more
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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)\} .
Janos, Ludvik, Martin, Harold W.
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Metric dimension of generalized wheels
Arab Journal of Mathematical Sciences, 2019 In a graph G, a vertex w∈V(G)resolves a pair of vertices u,v∈V(G)if d(u,w)≠d(v,w). A resolving set of G is a set of vertices S such that every pair of distinct vertices in V(G)is resolved by some vertex in S.
Badekara Sooryanarayana +2 more
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On the Dominant Local Resolving Set of Vertex Amalgamation Graphs
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Basically, the new topic of the dominant local metric dimension which be symbolized by Ddim_l (H) is a combination of two concepts in graph theory, they were called the local metric dimension and dominating set. There are some terms in this topic that is
Reni Umilasari +3 more
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