Results 221 to 230 of about 1,645 (243)

Fault-tolerant metric dimension of two-fold heptagonal-nonagonal circular ladder

Discrete Mathematics, Algorithms and Applications, 2021
The 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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Rotationally symmetrical plane graphs and their Fault-tolerant metric dimension

Annals of the University of Craiova - Mathematics and Computer Science Series, 2021
Consider 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 Generalised Petersen Graph P(n,3)

International Journal of Applied and Computational Mathematics
Vijay Kumar Bhat, Bhat Vijay Kumar
exaly   +3 more sources

On Metric Dimension and Fault Tolerant Metric Dimension of Some Chemical Structures

Polycyclic Aromatic Compounds, 2021
In chemistry, customary depiction for the structure of chemical compounds are graphs where the vertices and edges represents the atoms and bonds types, respectively.
Muhammad Faisal Nadeem, Ayesha Shabbir, Muhammad Azeem   +2 more
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On study of some bounds for fault-tolerant metric dimension and adjacency fault-tolerant resolving set of corona product graphs

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, Nasir Ali, Suhad Ali Osman Abdallah, N. S. Abd EL-Gawaad   +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 Applications
The 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, S. Angelin Kavitha Raj   +1 more
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Fault-tolerant strong metric dimension of graphs

Discrete Mathematics, Algorithms and Applications, 2022
In 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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Fault-Tolerant Strong Metric Dimension of Rooted Product Graphs

Communications on Applied Nonlinear Analysis
The 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
H. Prathab, S. Chandrasekaran, S. Krishnan   +2 more
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Some Symmetrical Planar Structures with their Fault-Tolerant Metric Dimension

Theory of Computing Systems
Sunny Kumar Sharma, Vijay Kumar Bhat, Latif Hanna, Maryam Al-Kandari   +3 more
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Fault-tolerant metric dimension of P(n, 2)ʘK 1 graph

, 2021
An ordered set W of vertices in a graph G is said to resolve G if every vertex in G is uniquely determined by its vector of distances to the vertices in W.
Z. Ahmad, Maqbool Chaudhary, A. Q. Baig, M. Zahid   +3 more
semanticscholar   +1 more source