Results 21 to 30 of about 2,452,302 (284)
On graphs with the maximum edge metric dimension
Discrete Applied Mathematics, 2019 An edge metric generator of a connected graph G is a vertex subset S for which every two distinct edges of G have distinct distance to some vertex of S , where the distance between a vertex v and an edge e is defined as the minimum of distances between v
Andrej Taranenko +2 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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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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Edge metric dimension of $k$ multiwheel graph
Rocky Mountain Journal of Mathematics, 2020 If we consider G=(V,E) to be a connected graph, with v∈V and e=uw∈E, then dG(e,v)= min{dG(u,v),dG(w,v)} has been defined as the distance between a vertex v and an edge e.
Zahid Raza
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Bi-Edge Metric Dimension of Graphs [PDF]
International Journal of Computing Science and Applied MathematicsGiven a connected G = (V(G),E(G)) graph. The main problem in graph metric dimensions is calculating the metric dimensions and their characterization.
Rinurwati Rinurwati +1 more
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Graphs with the edge metric dimension smaller than the metric dimension [PDF]
Applied Mathematics and Computation, 2020 Given a connected graph $G$, the metric (resp. edge metric) dimension of $G$ is the cardinality of the smallest ordered set of vertices that uniquely identifies every pair of distinct vertices (resp.
M. Knor +4 more
semanticscholar +5 more sources
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.
Pradeep Singh +3 more
semanticscholar +4 more sources
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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A note on the metric and edge metric dimensions of 2-connected graphs [PDF]
Discrete Applied Mathematics, 2022 12 ...
Martin Knor +2 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 $d_G(w,e_1)\ne d_G(w,e_2)$.
Ismael G Yero, Niko Tratnik
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