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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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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Fault-Tolerant Edge Metric Dimension of Zero-Divisor Graphs of Commutative Rings
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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Fault-tolerant edge metric dimension of certain families of graphs
AIMS Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaogang Liu +3 more
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On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs
Mathematics, 2022 Graphs of order n with fault-tolerant metric dimension n have recently been characterized.This paper points out an error in the proof of this characterization. We show that the complete multipartite graphs also have the fault-tolerant metric dimension n,
Sakander Hayat, Asad Khan, Yubin Zhong
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Computation of Edge Resolvability of Benzenoid Tripod Structure
Journal of Mathematics, 2021 In chemistry, graphs are commonly used to show the structure of chemical compounds, with nodes and edges representing the atom and bond types, respectively.
Ali Ahmad +4 more
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Fault-tolerant metric dimension of zero-divisor graphs of commutative rings
AKCE International Journal of Graphs and Combinatorics, 2021 Let R be a commutative ring with identity. The zero-divisor graph of R denoted by is an undirected graph where is the set of non-zero zero-divisors of R and there is an edge between the vertices z1 and z2 in if A set of vertices S resolves a graph G if ...
Sahil Sharma, Vijay Kumar Bhat
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Fault-Tolerant Partition Resolvability of Cyclic Networks
Journal of Mathematics, 2021 Graph invariants provide an amazing tool to analyze the abstract structures of networks. The interaction and interconnection between devices, sensors, and service providers have opened the door for an eruption of mobile over the web applications ...
Kamran Azhar +3 more
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Fault-Tolerant Metric Dimension (FTMD) of M-polynomial of Zigzag Edge Coronoid Fused by Starphene
, 2023 Abstract 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.
Umar Farooq +3 more
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