Metric-Based Resolvability of Quartz Structure

Singla, Chinu; Al‐Wesabi, Fahd N.; Pathania, Yash Singh; Alfurhood, Badria Sulaiman; Hilal, Anwer Mustafa; Rizwanullah, Mohammed; Hamza, Manar Ahmed; Mahzari, Mohammad

doi:10.32604/cmc.2022.022064

Cited by 8 publications

(4 citation statements)

References 45 publications

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“…Similarly, all the resolvability parameters for the benzenoid tripod structure are found in [ 31 ]. Metric resolvability and its fault-tolerant version for the Quartz structure found in [ 32 ]. An approximated version of the algorithm for computing the edge metric dimension is found in [ 33 ].…”

Section: Introductionmentioning

confidence: 99%

Edge based metric dimension of various coffee compounds

Ahmad,

Koam,

Azeem

et al. 2024

PLoS ONE

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An 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 systems. This research looked at a few coffee chemical structures in terms of edge locating numbers or edge metric size to better understand the mechanics of coffee molecules. Additionally, this research includes graph theoretical properties of coffee chemical structures. The chemicals found in coffee, such as caffeine, diterpene or cafestol, kahweol, chlorogenic, caffeic, gallotannins, and ellagitannins, are especially examined in these publications.

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Section: Introductionmentioning

confidence: 99%

Edge based metric dimension of various coffee compounds

Ahmad,

Koam,

Azeem

et al. 2024

PLoS ONE

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“…In [32], the internet graph and its fault-tolerant topology are covered. In [33], the notion of a fault-tolerant locating number is used to study a quartz structure, ref. [34] as well as the studies networks of connections associated to computers.…”

Section: Introductionmentioning

confidence: 99%

Notes on the Localization of Generalized Hexagonal Cellular Networks

2023

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The act of accessing the exact location, or position, of a node in a network is known as the localization of a network. In this methodology, the precise location of each node within a network can be made in the terms of certain chosen nodes in a subset. This subset is known as the locating set and its minimum cardinality is called the locating number of a network. The generalized hexagonal cellular network is a novel structure for the planning and analysis of a network. In this work, we considered conducting the localization of a generalized hexagonal cellular network. Moreover, we determined and proved the exact locating number for this network. Furthermore, in this technique, each node of a generalized hexagonal cellular network can be accessed uniquely. Lastly, we also discussed the generalized version of the locating set and locating number.

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“…In the realm of chemistry, the relevance of resolvability parameters resonates through numerous studies that leverage graph theory, with a particular emphasis on MD [20]. Its application has extended to the analysis of structures such as H-Naphtalenic and V C5C7 nanotubes [22], establishing upper bounds for cellulose networks [2], calculating the metric of silicate star structures [9], and investigating the MD of two-dimensional lattices of α-boron nanotubes [22]. Partition dimension has also left its mark on various structures, including the unique fullerene structure, bounded partition dimension for specific nanotubes, and partitioning bounds for polycyclic aromatic hydrocarbons [16].…”

Section: Introductionmentioning

confidence: 99%

Fault-Tolerant Metric Dimension (FTMD) of M-polynomial of Zigzag Edge Coronoid Fused by Starphene

Farooq,

Chudhary,

Afzal

et al. 2023

Preprint

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The application of graph invariants serves as a valuable tool for analyzing the complex structures of molecular graphs, attracting researchers across various fields. Graph theory has played a pivotal role in explaining chemical structures and finding practical applications. Representing chemical compounds as graphs enable theoretical exploration and yield meaningful insights. Among graph parameters, metric dimension stands out as a key metric, quantifying the minimum vertices needed for unique identification within a graph. The concept of fault-tolerant metric dimensions extends this idea, considering identification robustness in the face of faulty vertices or edges. This research applies metric dimension and fault-tolerant metric dimension to molecular graphs and networks, with a focus on the unique structural properties of the "M-polynomial of zigzag edge coronoid fused by starphene" molecule. Through graph theory, we deepen our understanding of this compound's intricate molecular architecture. Mathematics Subject Classification 2023: 05C12

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Metric-Based Resolvability of Quartz Structure

Cited by 8 publications

References 45 publications

Edge based metric dimension of various coffee compounds

Edge based metric dimension of various coffee compounds

Notes on the Localization of Generalized Hexagonal Cellular Networks

Fault-Tolerant Metric Dimension (FTMD) of M-polynomial of Zigzag Edge Coronoid Fused by Starphene

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