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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, Ali Ahmad, Muhammad Ibrahim, Muhammad Azeem   +3 more
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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.
Pradeep Singh, Sahil Sharma, Sunny Kumar Sharma, Vijay Kumar Bhat   +3 more
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On the edge metric dimension of some classes of cacti

AIMS Mathematics
The cactus graph has many practical applications, particularly in radio communication systems. Let $ G = (V, E) $ be a finite, undirected, and simple connected graph, then the edge metric dimension of $ G $ is the minimum cardinality of the edge metric ...
Lyimo Sygbert Mhagama , Muhammad Faisal Nadeem, Mohamad Nazri Husin   +2 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
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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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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, Zohaib Zahid, Dalal Alrowaili, Aiyared Iampan, Imran Siddique, Sohail Zafar   +5 more
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Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone [PDF]

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, Hassan Raza, Vijay Kumar Bhat   +2 more
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Edge Metric Dimension of Some Classes of Toeplitz Networks [PDF]

Journal of Mathematics, 2021
Toeplitz networks are used as interconnection networks due to their smaller diameter, symmetry, simpler routing, high connectivity, and reliability.
Dalal Alrowaili, Zohaib Zahid, Muhammad Ahsan, Sohail Zafar, Imran Siddique   +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, Jelena Sedlar, Riste Škrekovski   +2 more
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The K-Size Edge Metric Dimension of Graphs [PDF]

Journal of Mathematics, 2020
In this paper, a new concept k-size edge resolving set for a connected graph G in the context of resolvability of graphs is defined. Some properties and realizable results on k-size edge resolvability of graphs are studied.
Tanveer Iqbal, Muhammad Naeem Azhar, Syed Ahtsham Ul Haq Bokhary   +2 more
doaj   +3 more sources