Results 201 to 210 of about 684 (218)
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Fault-tolerant strong metric dimension of graphs
Discrete Mathematics, Algorithms and Applications, 2022In this paper, we introduce a variant of strong metric dimension, called the fault-tolerant strong metric dimension. A strong resolving set [Formula: see text] for [Formula: see text] is fault-tolerant if [Formula: see text] is also a strong resolving set, for each [Formula: see text] in [Formula: see text], and the fault-tolerant strong metric ...
Sathish Krishnan, Bharati Rajan
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Some Symmetrical Planar Structures with their Fault-Tolerant Metric Dimension
Theory of Computing SystemsVijay 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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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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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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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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Fault-tolerant dominant metric dimension of graphs
Asian-European Journal of MathematicsThe behavior of a graph via distance-based parameters has been widely used in various applications of daily life problems and in diverse disciplines including operation research, drug discovery, sensor networking, source localization, comparing interconnected networks, detection of network motifs, robot navigation, and image processing.
Imtiaz Ali, Muhammad Javaid, Yilun Shang
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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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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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Fault-tolerant metric dimension of the intersection graph of gamma sets in the zero-divisor graph
Discrete Mathematics, Algorithms and ApplicationsThe stable equivalent set is a finite collection of disjoint vertex subsets for a connected graph [Formula: see text] such that each set induces the same maximal independent set of [Formula: see text] and their union equals [Formula: see text]. The stable equivalence number is the maximum cardinality of the stable equivalent set [Formula: see text ...
S. Jeyamangala Abirami +1 more
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