Results 21 to 30 of about 20,240 (252)
Identifying the Exact Value of the Metric Dimension and Edge Dimension of Unicyclic Graphs
Mathematics, 2022 Given a simple connected graph G, the metric dimension dim(G) (and edge metric dimension edim(G)) is defined as the cardinality of a smallest vertex subset S⊆V(G) for which every two distinct vertices (and edges) in G have distinct distances to a vertex ...
Enqiang Zhu +2 more
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Graphs with the edge metric dimension smaller than the metric dimension [PDF]
Applied Mathematics and Computation, 2021 11 ...
Knor, Martin +4 more
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Computing edge version of metric dimension of certain chemical networks
Scientific ReportsIn the modern digital sphere, graph theory is a significant field of research that has a great deal of significance. It finds widespread application in computer science, robotic directions, and chemistry.
Muhammad Umer Farooq +5 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. In this article, we compute the metric and edge metric dimension of two classes of windmill graphs such as ...
Pradeep Singh +3 more
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On the metric dimension of Cayley graphs
AKCE International Journal of Graphs and Combinatorics, 2022 In this paper, we investigate the metric dimension, local metric dimension and edge metric dimension for some (generalized) Cayley graphs.
Afsaneh Rezaei +2 more
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Remarks on the Vertex and the Edge Metric Dimension of 2-Connected Graphs
Mathematics, 2022 The vertex (respectively edge) metric dimension of a graph G is the size of a smallest vertex set in G, which distinguishes all pairs of vertices (respectively edges) in G, and it is denoted by dim(G) (respectively edim(G)). The upper bounds dim(G)≤2c(G)−
Martin Knor +2 more
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Edge Metric Dimension of Some Graph Operations [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2019 Let $G=(V, E)$ be a connected graph. Given a vertex $v\in V$ and an edge $e=uw\in E$, the distance between $v$ and $e$ is defined as $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A nonempty set $S\subset V$ is an edge metric generator for $G$ if for any two edges $e_1,e_2\in E$ there is a vertex $w\in S$ such that $d_G(w,e_1)\ne d_G(w,e_2)$.
Peterin, Iztok, Yero, Ismael G.
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On Mixed Metric Dimension of Rotationally Symmetric Graphs
IEEE Access, 2020 A vertex u ∈ V(G) resolves (distinguish or recognize) two elements (vertices or edges) v, w ∈ E(G)UV(G) if dG(u, v) ≠ dG(u, w) . A subset Lm of vertices in a connected graph G is called a mixed metric generator for G if every two ...
Hassan Raza, Jia-Bao Liu, Shaojian Qu
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Metric dimension and edge metric dimension of unicyclic graphs
, 2021 The metric (resp. edge metric) dimension of a simple connected graph $G$, denoted by dim$(G)$ (resp. edim$(G)$), is the cardinality of a smallest vertex subset $S\subseteq V(G)$ for which every two distinct vertices (resp. edges) in $G$ have distinct distances to a vertex of $S$.
Zhu, Enqiang +2 more
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Vertex and edge metric dimensions of cacti
Discrete applied mathematics, 2022 In a graph G, a vertex (resp. an edge) metric generator is a set of vertices S such that any pair of vertices (resp. edges) from G is distinguished by at least one vertex from S. The cardinality of a smallest vertex (resp. edge) metric generator is the vertex (resp. edge) metric dimension of G. In [?] we determined the vertex (resp.
Jelena Sedlar, Riste Škrekovski
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