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Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid [PDF]
Mathematics, 2021 Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids.
Ali N. A. Koam +3 more
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On the Edge Metric Dimension of Certain Polyphenyl Chains [PDF]
Journal of Chemistry, 2021 The most productive application of graph theory in chemistry is the representation of molecules by the graphs, where vertices and edges of graphs are the atoms and valence bonds between a pair of atoms, respectively.
Muhammad Ahsan +5 more
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Asymptotic Behavior of the Edge Metric Dimension of the Random Graph [PDF]
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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Classes of Planar Graphs with Constant Edge Metric Dimension [PDF]
Complexity, 2021 The number of edges in a shortest walk (without repetition of vertices) from one vertex to another vertex of a connected graph G is known as the distance between them.
Changcheng Wei +4 more
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The dominant edge metric dimension of graphs
Electronic Journal of Graph Theory and Applications, 2023 For an ordered subset S = {v1, …, vk} of vertices in a connected graph G and an edge e′ of G, the edge metric S-representation of e′=ab is the vector rGe(e′|S)=(dG(e′,v1),…,dG(e′,vk)) , where dG(e′,vi)=min{dG(a, vi),dG(b, vi)}.
Mostafa Tavakoli +4 more
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Remarks on the Vertex and the Edge Metric Dimension of 2-Connected Graphs [PDF]
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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Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone
Frontiers in Physics, 2021 Minimum resolving sets (edge or vertex) have become an integral part of molecular topology and combinatorial chemistry. Resolving sets for a specific network provide crucial information required for the identification of each item contained in the ...
Sunny Kumar Sharma +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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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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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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