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On the strong metric dimension of the strong products of graphs
Open Mathematics, 2015 Let G be a connected graph. 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.
Kuziak Dorota +2 more
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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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Erratum to “On the strong metric dimension of the strong products of graphs”
Open Mathematics, 2015 The original version of the article was published in Open Mathematics (formerly Central European Journal of Mathematics) 13 (2015) 64–74. Unfortunately, the original version of this article contains a mistake: in Lemma 2.17 appears that for any C1-graph ...
Kuziak Dorota +2 more
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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 Local Metric Dimension of Strong Product Graphs [PDF]
Graphs and Combinatorics, 2015 A vertex $v\in V(G)$ is said to distinguish two vertices $x,y\in V(G)$ of a nontrivial connected graph $G$ if the distance from $v$ to $x$ is different from the distance from $v$ to $y$. A set $S\subset V(G)$ is a local metric generator for $G$ if every two adjacent vertices of $G$ are distinguished by some vertex of $S$.
Juan Alberto Rodríguez-Velázquez +1 more
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On the fractional strong metric dimension of graphs
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cong X Kang
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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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The strong metric dimension of the power graph of a finite group [PDF]
Discrete Applied Mathematics, 2018 We characterize the strong metric dimension of the power graph of a finite group. As applications, we compute the strong metric dimension of the power graph of a cyclic group, an abelian group, a dihedral group or a generalized quaternion group.
Min Feng, Xuanlong Ma
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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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Closed Formulae for the Strong Metric Dimension of Lexicographic Product Graphs
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
doaj +3 more sources