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Graphs with the edge metric dimension smaller than the metric dimension [PDF]
Applied Mathematics and Computation, 2021 11 ...
Riste Škrekovski +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 [19] we determined the vertex (resp.
Riste Škrekovski, Jelena Sedlar
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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 $d_G(w,e_1)\ne d_G(w,e_2)$.
Ismael Gonzalez Yero, Niko Tratnik
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Edge metric dimension and mixed metric dimension of a plane graph Tn
Discrete Mathematics, Algorithms and Applications, 2023Let [Formula: see text] be a connected graph where [Formula: see text] is the set of vertices of [Formula: see text] and [Formula: see text] is the set of edges of [Formula: see text]. The distance from the vertex [Formula: see text] to the edge [Formula: see text] is given by [Formula: see text].
Huige Shen, Jing Qu, Na Kang, Cong Lin
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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 $d_G(w,e_1)\ne d_G(w,e_2)$.
Ismael Gonzalez Yero, Iztok Peterin
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Vertices, edges, distances and metric dimension in graphs
Electronic Notes in Discrete Mathematics, 2016 Abstract Given a connected graph G = ( V , E ) , a set of vertices S ⊂ V is an edge metric generator for G , if any two edges of G are identified by S by mean of distances to the vertices in S . Moreover, in a natural way, S is a mixed metric generator, if any two elements of G (vertices or edges) are identified by S by
Ismael Gonzalez Yero
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Edge Version of Metric Dimension and Doubly Resolving Sets of the Necklace Graph
Mathematics, 2018 Consider an undirected and connected graph G = ( V G , E G ) , where V G and E G represent the set of vertices and the set of edges respectively.
Waqas Nazeer, Jia-Bao Liu, Zohaib Zahid
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On graphs with the maximum edge metric dimension
Discrete Applied Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrej Taranenko, Zehui Shao
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The effect of vertex and edge deletion on the edge metric dimension of graphs
Journal of Combinatorial Optimization, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lily Chen, Jun Yue, Meiqin Wei
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On Approximation Algorithm for the Edge Metric Dimension Problem
Theoretical Computer Science, 2019This article studies the concept of edge metric dimension. One can define the edge metric dimension as the smallest size of a vertex subset of a graph such that, for each pair of edges in the graph, there is a vertex in the subset which ``distinguishes'' the edges.
Yufei Huang 0010 +5 more
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