The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs [PDF]
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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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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Further new results on strong resolving partitions for graphs [PDF]
Open Mathematics, 2020 A set W of vertices of a connected graph G strongly resolves two different vertices x, y ∉ W if either d G(x, W) = d G(x, y) + d G(y, W) or d G(y, W) = d G(y, x) + d
Kuziak Dorota, Yero Ismael G.
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Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph [PDF]
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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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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Strong resolving graphs: The realization and the characterization problems [PDF]
Discrete Applied Mathematics, 2018 arXiv admin note: text overlap with arXiv:1508 ...
Dorota Kuziak +2 more
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The general position problem and strong resolving graphs
Open Mathematics, 2019 The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three pairwise distinct vertices from S lie on a common geodesic.
Klavžar Sandi, Yero Ismael G.
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A Study on Fuzzy Resolving Domination Sets and Their Application in Network Theory [PDF]
Mathematics, 2023 Consider a simple connected fuzzy graph (FG) G and consider an ordered fuzzy subset H = {(u1, σ(u1)), (u2, σ(u2)), …(uk, σ(uk))}, |H| ≥ 2 of a fuzzy graph; then, the representation of σ − H is an ordered k-tuple with regard to H of G. If any two elements
Manimozhi Vasuki +3 more
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Strong resolving partitions for strong product graphs and Cartesian product graphs
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ismael G Yero
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On the resolving strong domination number of some wheel related graphs
Journal of Physics: Conference Series, 2022 Abstract This study aims to analyse the resolving strong dominating set. This concept combinations of two notions, they are metric dimension and strong domination set. By a resolving strong domination set, we mean a set D s ⊂ V(G) which satisfies the definition of strong dominating set as well as resolving set.
R Humaizah +4 more
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