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Rotationally symmetrical plane graphs and their Fault-tolerant metric dimension
Annals of the University of Craiova - Mathematics and Computer Science Series, 2021Consider a robot which is investigating in a space exhibited by a graph (network), and which needs to know its current location. It can grant a sign to find how far it is from each among a lot of fixed places of interest (tourist spots or landmarks). We study the problem of calculating the minimum number of tourist spots required, and where they ought ...
Sunny Kumar Sharma, Vijay Kumar Bhat
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Fault Tolerant Metric Dimension of Arithmetic Graphs
Journal of Combinatorial Mathematics and Combinatorial ComputingFor a graph G , two vertices x , y ∈ G are said to be resolved by a vertex s ∈ G , if d ( x | s ) ≠ d ( y | s ) . The minimum cardinality of such a resolving set R in G is called its metric dimension. A resolving set R is said to be fault-tolerant, if for every p ∈ R , R − p preserves the property of being a resolving set.
Shoaib Sardar, Muhammad +5 more
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Fault-tolerant metric dimension of two-fold heptagonal-nonagonal circular ladder
Discrete Mathematics, Algorithms and Applications, 2021The problem of characterizing the classes of plane graphs with the bounded metric dimension, edge metric dimension, and fault-tolerant metric dimension is of great interest nowadays. In this paper, we study the metric dimension, the fault-tolerant metric dimension, and the edge metric dimension of a two-fold heptagonal-nonagonal circular ladder ...
Sunny Kumar Sharma, Vijay Kumar Bhat
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On the fault-tolerant metric dimension of convex polytopes
Applied Mathematics and Computation, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Raza, Hassan +2 more
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On fault-tolerant metric dimension of supramolecular networks
Discrete Mathematics, Algorithms and ApplicationsThe idea of a fault-tolerant metric dimension can be used in chemistry to examine a molecule’s structural resistance to the failure of particular atoms or chemical bonds. This is especially important when creating molecules for specific uses, like drug candidates, as they may be exposed to biological systems or the environment, which could cause ...
Hafiz Muhammad Afzal Siddiqui +3 more
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On the fault-tolerant metric dimension of certain interconnection networks
Journal of Applied Mathematics and Computing, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hassan Raza +2 more
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Fault-tolerant metric dimension of annihilator graphs of commutative rings
Summary: Let \(R\) be a commutative ring with identity. The annihilator graph \(AG (R)\) is a simple graph with vertex set as the set of all non-zero zero-divisors of \(R\), and two distinct vertices \(a\) and \(b\) are adjacent if and only if \(ann_R (a) \cup ann_R (b) \neq ann_R (a \cdot b)\).M S, AKHILA, K, Manilal
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On Metric Dimension and Fault Tolerant Metric Dimension of Some Chemical Structures
Polycyclic Aromatic Compounds, 2021Muhammad Faisal Nadeem +2 more
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Fault-Tolerant Strong Metric Dimension of Rooted Product Graphs
Communications on Applied Nonlinear AnalysisThe concept of fault tolerance in graph theory is critical in designing robust networks, ensuring that essential graph properties are preserved despite failures of vertices or edges. In this paper, we investigate the fault-tolerant strong metric dimension of rooted product graphs, a class of graphs derived by attaching multiple copies of a rooted graph
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Discrete Mathematics, Algorithms and Applications
In this paper, we investigate bounds for the fault-tolerant metric dimension and adjacency fault-tolerant resolving set of corona product graphs. Let [Formula: see text] and [Formula: see text] be two graphs with orders [Formula: see text] and [Formula: see text], respectively.
Muhammad Asif Shahzad +3 more
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In this paper, we investigate bounds for the fault-tolerant metric dimension and adjacency fault-tolerant resolving set of corona product graphs. Let [Formula: see text] and [Formula: see text] be two graphs with orders [Formula: see text] and [Formula: see text], respectively.
Muhammad Asif Shahzad +3 more
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