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Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid [PDF]
Mathematics, 2021 Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids.
Ali N. A. Koam +3 more
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Mixed metric dimension over (edge) corona products
AKCE International Journal of Graphs and Combinatorics, 2023 A subset S of V(G) is called a mixed resolving set for G if, for every two distinct elements x and y of [Formula: see text], there exists [Formula: see text] such that [Formula: see text].
M. Korivand +2 more
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Graphs with the edge metric dimension smaller than the metric dimension [PDF]
Applied Mathematics and Computation, 2021 11 ...
Martin Knor +2 more
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The dominant edge metric dimension of graphs
Electronic Journal of Graph Theory and Applications, 2023 For an ordered subset S = {v1, …, vk} of vertices in a connected graph G and an edge e′ of G, the edge metric S-representation of e′=ab is the vector rGe(e′|S)=(dG(e′,v1),…,dG(e′,vk)) , where dG(e′,vi)=min{dG(a, vi),dG(b, vi)}.
Mostafa Tavakoli +4 more
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Uniquely identifying the edges of a graph: The edge metric dimension [PDF]
Discrete Applied Mathematics, 2018 Let $G=(V,E)$ be a connected graph, let $v\in V$ be a vertex and let $e=uw\in E$ be an edge. The distance between the vertex $v$ and the edge $e$ is given by $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A vertex $w\in V$ distinguishes two edges $e_1,e_2\in E$ if $d_G(w,e_1)\ne d_G(w,e_2)$.
Niko Tratnik, Ismael G Yero
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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 $d_G(w,e_1)\ne d_G(w,e_2)$.
Iztok Peterin +2 more
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On the Edge Metric Dimension of Certain Polyphenyl Chains [PDF]
Journal of Chemistry, 2021 The most productive application of graph theory in chemistry is the representation of molecules by the graphs, where vertices and edges of graphs are the atoms and valence bonds between a pair of atoms, respectively.
Muhammad Ahsan +5 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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Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone
Frontiers in Physics, 2021 Minimum resolving sets (edge or vertex) have become an integral part of molecular topology and combinatorial chemistry. Resolving sets for a specific network provide crucial information required for the identification of each item contained in the ...
Sunny Kumar Sharma +2 more
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Asymptotic Behavior of the Edge Metric Dimension of the Random Graph
Discussiones Mathematicae Graph Theory, 2021 Given a simple connected graph G(V,E), the edge metric dimension, denoted edim(G), is the least size of a set S ⊆ V that distinguishes every pair of edges of G, in the sense that the edges have pairwise different tuples of distances to the vertices of S.
Zubrilina Nina
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