Results 11 to 20 of about 7,733 (263)

Fault-Tolerant Partition Resolvability of Cyclic Networks [PDF]

Journal of Mathematics, 2021
Graph invariants provide an amazing tool to analyze the abstract structures of networks. The interaction and interconnection between devices, sensors, and service providers have opened the door for an eruption of mobile over the web applications ...
Kamran Azhar, Sohail Zafar, Agha Kashif, Michael Onyango Ojiema   +3 more
doaj   +2 more sources

Further new results on strong resolving partitions for graphs [PDF]

Open Mathematics, 2020
A set W of vertices of a connected graph G strongly resolves two different vertices x, y ∉ W if either d G(x, W) = d G(x, y) + d G(y, W) or d G(y, W) = d G(y, x) + d
Kuziak Dorota, Yero Ismael G.
doaj   +4 more sources

The Application of Fault-Tolerant Partition Resolvability in Cycle-Related Graphs

Applied Sciences, 2022
The concept of metric-related parameters permeates all of graph theory and plays an important role in diverse networks, such as social networks, computer networks, biological networks and neural networks.
Kamran Azhar, Sohail Zafar, Agha Kashif, Amer Aljaedi, Umar Albalawi   +4 more
doaj   +2 more sources

The Mixed Partition Dimension: A New Resolvability Parameter in Graph Theory

IEEE Access
In this article, we introduce a novel graph-theoretical parameter called the mixed partition dimension and apply it to the path graph and the hexagonal network.
Siti Norziahidayu Amzee Zamri, Sikander Ali, Muhammad Azeem, Husam A. Neamah, Bandar Almohsen   +4 more
doaj   +2 more sources

Resolving dominating partitions in graphs [PDF]

Discrete Applied Mathematics, 2019
A partition $ =\{S_1,\ldots,S_k\}$ of the vertex set of a connected graph $G$ is called a \emph{resolving partition} of $G$ if for every pair of vertices $u$ and $v$, $d(u,S_j)\neq d(v,S_j)$, for some part $S_j$. The \emph{partition dimension} $ _p(G)$ is the minimum cardinality of a resolving partition of $G$.
Hernando Martín, María del Carmen, Mora Giné, Mercè, Pelayo Melero, Ignacio Manuel   +2 more
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Breast cancer chemical structures and their partition resolvability

Mathematical Biosciences and Engineering, 2022
<abstract><p>Cancer is a disease that causes abnormal cell formation and spreads throughout the body, causing harm to other organs. Breast cancer is the most common kind among many of cancers worldwide. Breast cancer affects women due to hormonal changes or genetic mutations in DNA.
Qingqun Huang, Adnan Khalil, Didar Abdulkhaleq Ali, Ali Ahmad, Ricai Luo, Muhammad Azeem   +5 more
openaire   +3 more sources

On the Fault Tolerant Partition Resolvability of Toeplitz Networks [PDF]

Mathematical Problems in Engineering, 2022
In any interconnection network, fault tolerance is the most desirable property to achieve reliability. Toeplitz networks are used as interconnection networks due their smaller diameter, symmetry, simpler routing, high connectivity, and reliability. The partition dimension of a network is presented as an extension of metric dimension of networks.
Asim Nadeem, Agha Kashif, Amer Aljaedi, Sohail Zafar   +3 more
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Fault Tolerant Partition Resolvability in Convex Polytopes

Mathematical Problems in Engineering, 2022
Convex polytopes are special types of polytopes having an additional property that they are also convex sets in the n-dimensional Euclidean space. The convex polytope topologies are being used in the antitracking networks due to their stability, resilience, and destroy-resistance.
Asim Nadeem, Agha Kashif, Ebenezer Bonyah, Sohail Zafar   +3 more
openaire   +1 more source

Subspace partitioning in human prefrontal cortex resolves cognitive interference

Proceedings of the National Academy of Sciences, 2022
AbstractHuman prefrontal cortex (PFC) constitutes the structural basis underlying flexible cognitive control, where mixed-selective neural populations encode multiple task-features to guide subsequent behavior. The mechanisms by which the brain simultaneously encodes multiple task-relevant variables while minimizing interference from task-irrelevant ...
Jan Weber, Gabriela Iwama, Anne-Kristin Solbakk, Alejandro O. Blenkmann, Pal G. Larsson, Jugoslav Ivanovic, Robert T. Knight, Tor Endestad, Randolph Helfrich   +8 more
openaire   +2 more sources

On Sharp Bounds on Partition Dimension of Convex Polytopes

IEEE Access, 2020
Let $\Omega $ be a connected graph and for a given $l$ -ordered partition of vertices of a connected graph $\Omega $ is represented as $\beta =\{\beta _{1},\beta _{2}, {\dots },\beta _{l}\}$ . The representation of a vertex $\mu \in V(\Omega)$ is
Yu-Ming Chu, Muhammad Faisal Nadeem, Muhammad Azeem, Muhammad Kamran Siddiqui   +3 more
doaj   +1 more source