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Antipodal Edge-Colorings of Hypercubes
Discussiones Mathematicae Graph Theory, 2019 Two vertices of the k-dimensional hypercube Qkare antipodal if they differ in every coordinate. Edges uv and xy are antipodal if u is antipodal to x and v is antipodal to y.
West Douglas B., Wise Jennifer I.
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Perfect Actions for Scalar Theories [PDF]
, 1997 We construct an optimally local perfect lattice action for free scalars of arbitrary mass, and truncate its couplings to a unit hypercube. Spectral and thermodynamic properties of this ``hypercube scalar'' are drastically improved compared to the ...
Bell +4 more
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Subcube embeddability and fault tolerance of augmented hypercubes
, 2008 Hypercube networks have received much attention from both parallel processing and communications areas over the years since they offer a rich interconnection structure with high bandwidth, logarithmic diameter, and high degree of fault tolerance.
Mohamed Yasim, Sithy Shameema
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Counting hypercubes in hypercubes
Discrete Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fermat surfaces and hypercubes
Mathematics and Systems Science, 2023 <p>Fermat’s last theorem appears not as a unique property of natural numbers but as the bottom line of extended possible issues involving larger dimensions and powers when observed from a natural vector space viewpoint. The fabric of this general Fermat’s theorem structure consists of a well-defined set of vectors associated with <strong> ...
Ramon Carbó-Dorca, Debraj Nath
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Spin Glasses on the Hypercube [PDF]
, 2009 We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the
B. Seoane +9 more
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Random subcube intersection graphs I: cliques and covering [PDF]
, 2015 We study random subcube intersection graphs, that is, graphs obtained by selecting a random collection of subcubes of a fixed hypercube $Q_d$ to serve as the vertices of the graph, and setting an edge between a pair of subcubes if their intersection is ...
Falgas-Ravry, Victor, Markström, Klas
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A general analytical model of adaptive wormhole routing in k-ary n-cubes [PDF]
, 2003 Several analytical models of fully adaptive routing have recently been proposed for k-ary n-cubes and hypercube networks under the uniform traffic pattern.
Ferguson, J.D. +2 more
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On the Area of Hypercube Layouts [PDF]
, 2001 This paper precisely analyzes the wire density and required area in standard layout styles for the hypercube. The most natural, regular layout of a hypercube of N^2 nodes in the plane, in a N x N grid arrangement, uses floor(2N/3)+1 horizontal wiring ...
Greenberg, Ronald I., Guan, Lee
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Neighborhood Broadcasting in Hypercubes
SIAM Journal on Discrete Mathematics, 2008 In the broadcasting problem, one node needs to broadcast a message to all other nodes in a network. If nodes can only communicate with one neighbor at a time, broadcasting takes at least $\lceil \log_2 N \rceil$ rounds in a network of $N$ nodes. In the neighborhood broadcasting problem, the node that is broadcasting needs to inform only its neighbors ...
Bermond, Jean-Claude +3 more
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