Results 41 to 50 of about 27,973 (272)
On Sharp Bounds of Fault-Tolerant Partition Dimension of Convex Polytopes
Scientific Annals of Computer ScienceGraph theory is a fundamental and powerful tool for designing and modeling networks. It plays a vital role in diverse real-world systems, including social, computer, biological, ecological, and neural networks.
Kamran Azhar, Asim Nadeem, Yilun Shang
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On the dimension of downsets of integer partitions and compositions [PDF]
Australas. J Comb., 2017 We characterize the downsets of integer partitions (ordered by containment of Ferrers diagrams) and compositions (ordered by the generalized subword order) which have finite dimension in the sense of Dushnik and Miller. In the case of partitions, while the set of all partitions has infinite dimension, we show that every proper downset of partitions has
Michael Engen, Vincent Vatter
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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 +3 more
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The Partition Dimension of a Path Graph
, 2021 Resolving partition is part of graph theory. This article, explains about resolving partition of the path graph, with. Given a connected graph  and  is a subset of  writen .
Rahmi, Fathur, Ramdhani, Vivi
core
Family of Graphs with Partition Dimension Three
Indonesian Journal of CombinatoricsThe characterization of all connected graphs of order n ≥3 with partition dimension 2, n−1 or n has been completely done. Additionally, all connected graphs of order n≥9 with partition dimension n−2 and graphs of order n≥11 with partition dimension n−3 ...
Debi Oktia Haryeni +2 more
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Bounds on partition dimension of Peterson graphs
, 2021 The distance of a connected, simple graph P is denoted by d(eta(1), eta(2)), which is the length of a shortest path between the vertices eta(1), eta(2) is an element of V(P), where V(P) is the vertex set of P. The l- ordered partition of V(P) is theta = (
Azeem, Muhammasd +9 more
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Diversity and complexity in neural organoids
FEBS Letters, EarlyView.Neural organoid research aims to expand genetic diversity on one side and increase tissue complexity on the other. Chimeroids integrate multiple donor genomes within single organoids. Self‐organising multi‐identity organoids, exogenous cell seeding, or enforced assembly of region‐specific organoids contribute to tissue complexity.
Ilaria Chiaradia, Madeline A. Lancaster
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On the k-partition dimension of graphs
, 2018 As a generalization of the concept of the partition dimension of a graph, this article introduces the notion of the k-partition dimension. Given a nontrivial connected graph G=(V,E), a partition II of V is said to be a k-partition generator of G if any ...
Estrada Moreno, Alejandro
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On Dimension Partitions in Discrete Metric Spaces [PDF]
, 2013 Let (W,d) be a metric space and S={s1 …sk} an ordered list of subsets of W. The distance between p∈W and si∈S is d(p, si)= min { d(p,q) : q∈si }. S is a resolving set for W if d(x, si)=d(y, si) for all si implies x=y. A metric basis is a resolving set of minimal cardinality, named the metric dimension of (W,d). The metric dimension has been extensively
Fabien Rebatel, Edouard Thiel
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FEBS Letters, EarlyView.Mitochondrial remodeling shapes neural and glial lineage progression by matching metabolic supply with demand. Elevated OXPHOS supports differentiation and myelin formation, while myelin compaction lowers mitochondrial dependence, revealing mitochondria as key drivers of developmental energy adaptation.
Sahitya Ranjan Biswas +3 more
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