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The dominant edge metric dimension of graphs
Electronic Journal of Graph Theory and Applications, 2023 Summary: For an ordered subset \(S = \{v_1, \dots, v_k\}\) of vertices in a connected graph \(G\) and an edge \(e'\) of \(G\), the edge metric \(S\)-representation of \(e'=ab\) is the vector \(r_G^e(e'|S)=(d_G(e',v_1),\dots,d_G(e',v_k))\), where \(d_G(e',v_i)=\min\{d_G(a, v_i),d_G(b,v_i)\}\). A dominant edge metric generator for \(G\) is a vertex cover
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 $d_G(w,e_1)\ne d_G(w,e_2)$.
Aleksander Kelenc +2 more
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Identifying the Exact Value of the Metric Dimension and Edge Dimension of Unicyclic Graphs [PDF]
Discrete Applied Mathematics, 2022 In a graph G, the cardinality of the smallest ordered set of vertices that distinguishes every element of V (G) (resp. E(G)) is called the vertex (resp. edge) metric dimension of G. In [16] it was shown that both vertex and edge metric dimension of a unicyclic graph G always take values from just two explicitly given consecutive integers that are ...
Enqiang Zhu +2 more
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Patched Network and Its Vertex-Edge Metric-Based Dimension [PDF]
IEEE Access, 2023 The p-type networks are designed with the help of CVNET at topo group Cluj and also given support by nano studio. Such networks develop new p-type surfaces and also represent the decorations of the surfaces.
Sidra Bukhari +3 more
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On the Edge Metric Dimension of Different Families of Möbius Networks [PDF]
Mathematical Problems in Engineering, 2021 For an ordered subset Q e of vertices in a simple connected graph
Bo Deng +2 more
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Fault-Tolerant Edge Metric Dimension of Zero-Divisor Graphs of Commutative Rings [PDF]
AxiomsIn recent years, the intersection of algebraic structures and graph-theoretic concepts has developed significant interest, particularly through the study of zero-divisor graphs derived from commutative rings.
Omaima Alshanquiti +2 more
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Edge Metric Dimension and Edge Basis of One-Heptagonal Carbon Nanocone Networks
IEEE Access, 2022 A molecular (chemical) graph is a simple connected graph, where the vertices represent the compound’s atoms and the edges represent bonds between the atoms, and the degree (valence) of every vertex (atom) is not more than four.
Karnika Sharma +2 more
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Metric dimension and edge metric dimension of unicyclic graphs [PDF]
, 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 $S$.
Enqiang Zhu +2 more
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On the edge metric dimension for the random graph [PDF]
, 2016 Let $G(V, E)$ be a connected simple undirected graph. In this paper we prove that the edge metric dimension (introduced by Kelenc, Tratnik and Yero) of the Erd s-R nyi random graph $G(n, p)$ is given by: $$\textrm{edim}(G(n, p)) = (1 + o(1))\frac{4\log(n)}{\log(1/q)},$$ where $q = 1 - 2p(1-p)^2(2-p)$.
Nina Zubrilina
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Edge metric dimension of some Cartesian product of graphs
Proyecciones (Antofagasta)The edge metric dimension edim(G)of a connected graph G is the minimum cardinality of a set S of vertices such that each edge is uniquely determined by its distance from the vertices of the set S. In this work, the edge metric dimension of the prism over
Saritha Chandran C., T. Reji
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