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
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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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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 +2 more
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Edge Metric Dimension and Edge Basis of One-Heptagonal Carbon Nanocone Networks [PDF]
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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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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Metric and Edge Metric Dimension of Zigzag Edge Coronoid Fused with Starphene [PDF]
, 2021 Let $ =(V,E)$ be a simple connected graph. $d( , )=min\{d( , w), d( , d\}$ computes the distance between a vertex $ \in V( )$ and an edge $ =wd\in E( )$. A single vertex $ $ is said to recognize (resolve) two different edges $ _{1}$ and $ _{2}$ from $E( )$ if $d( , _{2})\neq d( , _{1}\}$.
Sunny Kumar Sharma +3 more
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Graphs with the edge metric dimension smaller than the metric dimension [PDF]
Applied Mathematics and Computation, 2021 11 ...
Martin Knor +4 more
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Fault-Tolerant Edge Metric Dimension of Zero-Divisor Graphs of Commutative Rings [PDF]
AxiomsIn recent years, the intersection of algebraic structures and graph-theoretic concepts has developed significant interest, particularly through the study of zero-divisor graphs derived from commutative rings.
Omaima Alshanquiti +2 more
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Identifying the Exact Value of the Metric Dimension and Edge Dimension of Unicyclic Graphs [PDF]
Discrete Applied Mathematics, 2022 In a graph G, the cardinality of the smallest ordered set of vertices that distinguishes every element of V (G) (resp. E(G)) is called the vertex (resp. edge) metric dimension of G. In [16] it was shown that both vertex and edge metric dimension of a unicyclic graph G always take values from just two explicitly given consecutive integers that are ...
Enqiang Zhu +2 more
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