Results 21 to 30 of about 253,596 (293)

The dominant edge metric dimension of graphs [PDF]

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, Meysam Korivand, Ahmad Erfanian, Gholamreza Abrishami, Edy Tri Baskoro   +4 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 $d_G(w,e_1)\ne d_G(w,e_2)$.
Iztok Peterin, Ismael G. Yero
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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, Shaoxiang Peng, Chanjuan Liu   +2 more
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Barycentric Subdivision of Cayley Graphs With Constant Edge Metric Dimension [PDF]

IEEE Access, 2020
A motion of a robot in space is represented by a graph. A robot change its position from point to point and its position can be determined itself by distinct labelled landmarks points.
Ali N. A. Koam, Ali Ahmad
doaj   +2 more sources

The local edge metric dimension of graph

Journal of Physics: Conference Series, 2020
Abstract In this paper, we introduce a new notion of graph theory study, namely a local edge metric dimension. It is a natural extension of metric dimension concept. dG (e,v) = min{d(x,v),d(y,v)} is the distance between the vertex v and the edge xy in graph G. A non empty set
Robiatul Adawiyah, Dafik Dafik, Ridho Alfarisi, Rafiantika Megahnia Prihandini, Ika Hesti Agustin, M. Venkatachalam   +5 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, K. Khashyarmanesh, M. Tavakoli   +2 more
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Edge Metric Dimension of Some Generalized Petersen Graphs [PDF]

Results in Mathematics, 2019
The edge metric dimension problem was recently introduced, which initiated the study of its mathematical properties. The theoretical properties of the edge metric representations and the edge metric dimension of generalized Petersen graphs $GP(n,k)$ are studied in this paper. We prove the exact formulae for $GP(n,1)$ and $GP(n, 2)$, while for the other
Vladimir Filipović, Aleksandar Kartelj, Jozef Kratica   +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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Optimizing emergency response services in urban areas through the fault-tolerant metric dimension of hexagonal nanosheet [PDF]

Scientific Reports
In this work, we find the fault-tolerant metric dimension of a hexagonal nanosheet. This concept ensures robust identity of vertices inside a graph, even in situations in which a few resolving vertices fail.
Yaoyao Tu, Sikander Ali, Muhammad Azeem, Misbah Arshad, Ghulam Haidar, Hamdy Khamees Thabet   +5 more
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On the edge metric dimension of graphs

AIMS Mathematics, 2020
Let $G=(V,E)$ be a connected graph of order $n$. $S \subseteq V$ is an edge metric generator of $G$ if any pair of edges in $E$ can be distinguished by some element of $S$.
Meiqin Wei, Jun Yue, Xiaoyu zhu
doaj   +3 more sources