Results 11 to 20 of about 74,479 (279)
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.
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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 +2 more
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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 +3 more
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A note on the partition dimension of Cartesian product graphs
Applied Mathematics and Computation, 2010 Let $G=(V,E)$ be a connected graph. The distance between two vertices $u,v\in V$, denoted by $d(u, v)$, is the length of a shortest $u-v$ path in $G$. The distance between a vertex $v\in V$ and a subset $P\subset V$ is defined as $min\{d(v, x): x \in P\}$
Rodriquez-Velazquez, Juan A. +1 more
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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 +4 more
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The Mixed Partition Dimension: A New Resolvability Parameter in Graph Theory
IEEE AccessIn 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 +4 more
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Structural Analysis of Octagonal Nanotubes via Double Edge-Resolving Partitions
ProcessesIn materials science, the open nanotube derived from an octagonal grid is one of the most important and extensively researched compounds. Finding strategies for representing a variety of chemical compounds so that different compounds can have different representations is necessary for the investigation of chemical structures.
Amal S. Alali +2 more
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Strong resolving partitions for strong product graphs and Cartesian product graphs
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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 +5 more
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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 +3 more
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