Fault-Tolerant Resolvability and Extremal Structures of Graphs
Mathematics, 2019 In this paper, we consider fault-tolerant resolving sets in graphs. We characterize n-vertex graphs with fault-tolerant metric dimension n, n − 1 , and 2, which are the lower and upper extremal cases.
Hassan Raza +3 more
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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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Robust mesh generation for electromagnetic models with geometric defects through node alignment and mesh boolean operations [PDF]
Scientific ReportsThis paper presents a mesh fault-tolerant repair algorithm tailored to address common geometric issues inherent in electromagnetic models. During the actual production design phase, electromagnetic models frequently display a variety of geometric ...
Z. H. Gao +5 more
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All metric bases and fault-tolerant metric dimension for square of grid [PDF]
Opuscula Mathematica, 2022 For a simple connected graph \(G=(V,E)\) and an ordered subset \(W = \{w_1,w_2,\ldots, w_k\}\) of \(V\), the code of a vertex \(v\in V\), denoted by \(\mathrm{code}(v)\), with respect to \(W\) is a \(k\)-tuple \((d(v,w_1),\ldots, d(v, w_k))\), where \(d ...
Laxman Saha +2 more
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Fault-Tolerant Fuzzy Resolving Domination Set
International Journal of Applied and Computational MathematicsLenka Čepová, Elangovan Muniyandy
exaly +2 more sources
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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Studies of Multilevel Networks via Fault-Tolerant Metric Dimensions
IEEE Access, 2022 A subset $T$ of the vertex set of a network $G$ is called a resolving set for $G$ if each pair of vertices of $G$ have distinct representations with respect to $T$ . A resolving set $B^{\prime} $ among all the resolving sets of a network $G$
Imtiaz Ali +2 more
doaj +1 more source
Distributed control of a fault tolerant modular multilevel inverter for direct-drive wind turbine grid interfacing [PDF]
, 2012 Modular generator and converter topologies are being pursued for large offshore wind turbines to achieve fault tolerance and high reliability. A centralized controller presents a single critical point of failure which has prevented a truly modular and ...
Finney, Stephen J. +4 more
core +4 more sources
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
doaj +1 more source
An application of adaptive fault-tolerant control to nano-spacecraft [PDF]
, 2014 Since nano-spacecraft are small, low cost and do not undergo the same rigor of testing as conventional spacecraft, they have a greater risk of failure.
Biggs, James, Han, Yu, Cui, Naigang
core +3 more sources