Metric, edge-metric, mixed-metric, and fault-tolerant metric dimensions of geometric networks with potential applications [PDF]
Scientific ReportsResolvability parameters of graphs are widely applicable in fields like computer science, chemistry, and geography. Many of these parameters, such as the metric dimension, are computationally hard to determine. This paper focuses on Möbius-type geometric
Sakander Hayat +6 more
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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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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 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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Optimizing emergency response services in urban areas through the fault-tolerant metric dimension of hexagonal nanosheet [PDF]
Scientific ReportsIn 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 +5 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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Edge based metric dimension of various coffee compounds.
PLoS ONEAn important dietary source of physiologically active compounds, coffee also contains phenolic acids, diterpenes, and caffeine. According to a certain study, some coffee secondary metabolites may advantageously modify a number of anti-cancer defense ...
Ali Ahmad +4 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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Exploring metric dimension of nanosheets, nanotubes, and nanotori of SiO2. [PDF]
PLoS ONEThis work investigates the metric dimension (MD) and edge metric dimension (EMD) of SiO2 nanostructures, specifically nanosheets, nanotubes, and nanotorii.
Umar Farooq +4 more
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Identifying the Exact Value of the Metric Dimension and Edge Dimension of Unicyclic Graphs
Mathematics, 2022 Given a simple connected graph G, the metric dimension dim(G) (and edge metric dimension edim(G)) is defined as the cardinality of a smallest vertex subset S⊆V(G) for which every two distinct vertices (and edges) in G have distinct distances to a vertex ...
Enqiang Zhu +2 more
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