Results 191 to 200 of about 844 (217)
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Planarity for clustered graphs
1995In this paper, we introduce a new graph model known as clustered graphs, i.e. graphs with recursive clustering structures. This graph model has many applications in informational and mathematical sciences. In particular, we study C-planarity of clustered graphs.
Qing-Wen Feng +2 more
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Aromaticity of Planar Boron Clusters Confirmed
Journal of the American Chemical Society, 2005Low-energy boron clusters are characterized by two-dimensional geometry. Aromaticity of these planar boron clusters was established in terms of topological resonance energy (TRE). All planar boron clusters were found to be highly aromatic with large positive TREs even if they have 4n pi-electrons.
Jun-ichi, Aihara +2 more
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Planar soap bubble clusters with a cavity
The European Physical Journal E, 2007We construct local energy-minimizing bubble clusters in the plane that are not simply-connected. Numerical evidence suggests that these minima are not isolated.
C E, Garza-Hume, P, Padilla
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Planar graph routing on geographical clusters
Ad Hoc Networks, 2005Geographic routing protocols base their forwarding decisions on the location of the current device, its neighbors, and the packets destination. Early proposed heuristic greedy routing algorithms might fail even if there is a path from source to destination.
Hannes Frey, Daniel Görgen
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Hierarchical clustering with planar segments as prototypes
Pattern Recognition Letters, 2015Abstract Clustering methods divide a set of observations into groups in such a way that members of the same group are more similar to one another than to the members of the other groups. One of the scientifically well known methods of clustering is the hierarchical agglomerative one.
Jacek M. Leski, Marian Kotas
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The σ delocalization in planar boron clusters
Dalton Transactions, 2009The sigma delocalization plays an important role in the stability of small boron clusters; therefore, it is important to establish under which circumstances this delocalization contributes to the aromaticity of these molecules. In this work, using electron localization function (ELF) calculations, we show that sigma and pi electrons follow different ...
Luis, Rincon +5 more
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How to draw a planar clustered graph
1995In this paper, we introduce and show how to draw a practical graph structure known as clustered graphs. We present an algorithm which produces planar, straight-line, convex drawings of clustered graphs in O(n2.5) time. We also demonstrate an area lower bound and an angle upper bound for straight-line convex drawings of C-planar graphs.
Qing-Wen Feng +2 more
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Beyond Clustered Planar Graphs
2020Many real-world networks exhibit an inherent clustering structure, which may arise from the presence of communities inside the network or from semantic affinities among nodes. Constructing effective visualizations for such networks is a crucial task that poses several practical and theoretical challenges.
Angelini, Patrizio, Da Lozzo, Giordano
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Planar clusters and perimeter bounds
Philosophical Magazine, 2005We provide upper and lower bounds on the least-perimeter way to enclose and separate n regions of equal area in the plane (theorem 3.1). Along the way, inside the hexagonal honeycomb, we provide minimizers for each n (theorem 2.7).
A. Heppes, F. Morgan *
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Planar Tetracoordinate Fluorine in Binary Clusters
ChemPhysChemPlanar tetracoordinate fluorine (ptF) species are rare and exotic due to the extreme electronegativity of fluorine. Herein, a ptF species is predicted in the binary Li4F4− and Na4F4− clusters. The global minimum of the clusters features C2v geometry and are stabilized by significant electrostatic interaction. Moreover, multicenter ionic bonds also play
Kangkan Sarmah +3 more
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