Results 11 to 20 of about 1,645 (243)
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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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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FAULT-TOLERANT METRIC DIMENSION OF CIRCULANT GRAPHS [PDF]
Facta Universitatis, Series: Mathematics and Informatics, 2019 A set $W$ of vertices in a graph $G$ is called a resolving setfor $G$ if for every pair of distinct vertices $u$ and $v$ of $G$ there exists a vertex $w \in W$ such that the distance between $u$ and $w$ is different from the distance between $v$ and $w$. The cardinality of a minimum resolving set is called the metric dimension of $G$, denoted by $\beta(
Seyedi, Narjes, Maimani, Hamid Reza
semanticscholar +3 more sources
The fault-tolerant metric dimension of the king’s graph [PDF]
Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, 2017 The concept of resolving the set within a graph is related to the optimal placement problem of access points in an indoor positioning system. A vertex w of the undirected connected graph G resolves the vertices u and v of G if the distance between ...
Voronov Roman Vladimirovich
exaly +4 more sources
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 Metric Dimension in Carbon Networks
FoundationsIn this paper, we study the fault-tolerant metric dimension in graph theory, an important measure against failures in unique vertex identification. The metric dimension of a graph is the smallest number of vertices required to uniquely identify every ...
Kamran Azhar, Asim Nadeem, Yilun Shang
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Fault-Tolerant Metric Dimension of Cube of Paths
Journal of Physics: Conference Series, 2021 Abstract For a simple connected graph G = (V (G), E(G)), a set R ⊆ V (G) is said to be a resolving set of G if every pair of vertices of G are resolved by some vertices in R i.e., every pair of vertices of G are identified uniquely by some vertex elements in F.
Laxman Saha
exaly +3 more sources
Fault-Tolerant Metric Dimension and Applications: Zero-Divisor Graph of Upper Triangular Matrices
MathematicsGraph invariants play a crucial role in understanding the structural and combinatorial characteristics of graphs. The fault-tolerant metric dimension, as a significant graph invariant, finds applications in diverse areas such as robust network ...
Latif Abdelmalek Hanna +2 more
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The Fault-Tolerant Metric Dimension of Cographs [PDF]
International Symposium on Fundamentals of Computation Theory, 2019 arXiv admin note: text overlap with arXiv:1806 ...
Duygu Vietz, Egon Wanke
semanticscholar +4 more sources
Investigating the Metric and Fault-Tolerant Dimensions in Para-Line Network Topologies
AKCE International Journal of Graphs and CombinatoricsThe resolving set (RS) and metric dimension (MD) are critical concepts used in various fields such as computer networks, robot navigation, chemical structures, communication networks, transportation, and electric circuits.
M. Faheem +5 more
doaj +3 more sources