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The Simultaneous Strong Resolving Graph and the Simultaneous Strong Metric Dimension of Graph Families [PDF]
Mathematics, 2020 We consider in this work a new approach to study the simultaneous strong metric dimension of graphs families, while introducing the simultaneous version of the strong resolving graph.
Ismael González Yero
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Local Fractional Strong Metric Dimension of Certain Complex Networks
Complexity, 2023 Fractional variants of distance-based parameters have application in the fields of sensor networking, robot navigation, and integer programming problems.
Faiza Jamil +3 more
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Metric Dimension, Minimal Doubly Resolving Sets, and the Strong Metric Dimension for Jellyfish Graph and Cocktail Party Graph [PDF]
Complexity, 2020 Let Γ be a simple connected undirected graph with vertex set VΓ and edge set EΓ. The metric dimension of a graph Γ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely ...
Jia-Bao Liu, Ali Zafari, Hassan Zarei
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Local Fractional Strong Metric Dimension of Certain Rotationally Symmetric Planer Networks
IEEE Access, 2021 Fractional versions of metric based networks invariants widen the scope of application in fields of intelligent systems, computer science and chemistry including, robot navigation, sensor networking, linear optimization problems, scheduling, assignment ...
Faiza Jamil +4 more
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The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs
Mathematics, 2020 A vertex w of a connected graph G strongly resolves two distinct vertices u,v∈V(G), if there is a shortest u,w path containing v, or a shortest v,w path containing u. A set S of vertices of G is a strong resolving set for G if every two distinct vertices
Dorota Kuziak
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Metric and strong metric dimension in TI-power graphs of finite groups
AIMS MathematicsGiven a finite group $ G $ with the identity $ e $, the TI-power graph (trivial intersection power graph) of $ G $ is an undirected graph with vertex set $ G $, in which two distinct vertices $ x $ and $ y $ are adjacent if $ \langle x\rangle\cap \langle
Chunqiang Cui, Jin Chen, Shixun Lin
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Closed Formulae for the Strong Metric Dimension of Lexicographic Product Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2016 Given a connected graph G, a vertex w ∈ V (G) strongly resolves two vertices u, v ∈ V (G) if there exists some shortest u − w path containing v or some shortest v − w path containing u. A set S of vertices is a strong metric generator for G if every pair
Kuziak Dorota +2 more
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Bounded Variation Separates Weak and Strong Average Lipschitz [PDF]
EntropyWe closely examine a recently introduced notion of average smoothness. The latter defined a weak and strong average-Lipschitz seminorm for real-valued functions on general metric spaces.
Ariel Elperin, Aryeh Kontorovich
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Strong metric dimension: A survey [PDF]
Yugoslav Journal of Operations Research, 2014 The strong metric dimension has been a subject of considerable amount of research in recent years. This survey describes the related development by bringing together theoretical results and computational approaches, and places the recent results
Kratica Jozef +3 more
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Complexity, 2020 Let G be a finite, connected graph of order of, at least, 2 with vertex set VG and edge set EG. A set S of vertices of the graph G is a doubly resolving set for G if every two distinct vertices of G are doubly resolved by some two vertices of S.
Jia-Bao Liu, Ali Zafari
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