Results 201 to 210 of about 718 (221)

On the fault-tolerant metric dimension of certain interconnection networks

Journal of Applied Mathematics and Computing, 2018
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Hassan Raza, Sakander Hayat, Xiang-Feng Pan   +2 more
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Fault Tolerant Metric Dimension of Arithmetic Graphs

Journal of Combinatorial Mathematics and Combinatorial Computing
For 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, Rasheed, Komal, Cancan, Murat, Farahani, Mohammad Reza, Alaeiyan, Mehdi, Patil, Shobha V.   +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, 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 circulant graphs C(1,2,3)

Theoretical Computer Science, 2020
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Mithun Basak, Laxman Saha, Gour Kanta Das, Kalishankar Tiwary   +3 more
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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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Fault-tolerant dominant metric dimension of graphs

Asian-European Journal of Mathematics
The 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, 2021
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 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
exaly   +2 more sources

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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