Results 11 to 20 of about 254,578 (267)
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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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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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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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
Filipović, Vladimir +2 more
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Patched Network and Its Vertex-Edge Metric-Based Dimension
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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Mixed metric dimension of graphs with edge disjoint cycles [PDF]
Discrete Applied Mathematics, 2021 In a graph G, the cardinality of the smallest ordered set of vertices that distinguishes every element of V (G)[E(G) is called the mixed metric dimension of G. In this paper we first establish the exact value of the mixed metric dimension of a unicycic graph G which is derived from the structure of G.
Jelena Sedlar, Riste Škrekovski
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Barycentric Subdivision of Cayley Graphs With Constant Edge Metric Dimension
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
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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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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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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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