Results 31 to 40 of about 19,522 (124)
Fault-Tolerant Panconnectivity of Augmented Cubes AQn
International Journal of Foundations of Computer Science, 2019 The augmented cube [Formula: see text] is a variation of the hypercube [Formula: see text]. This paper considers the fault-tolerant Panconnectivity of [Formula: see text]. Assume that [Formula: see text] and [Formula: see text]. We prove that for any two fault-free vertices [Formula: see text] and [Formula: see text] with distance [Formula: see text ...
Xirong Xu +3 more
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Trimmed Serendipity Finite Element Differential Forms
, 2018 We introduce the family of trimmed serendipity finite element differential form spaces, defined on cubical meshes in any number of dimensions, for any polynomial degree, and for any form order. The relation between the trimmed serendipity family and the (
Gillette, Andrew, Kloefkorn, Tyler
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Fractional matching preclusion for generalized augmented cubes
Discrete Mathematics & Theoretical Computer Science, 2019 The \emph{matching preclusion number} of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu recently introduced the concept of fractional matching preclusion number.
Tianlong Ma +3 more
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Fault-tolerant analysis of augmented cubes
, 2012 The augmented cube $AQ_n$, proposed by Choudum and Sunitha [S. A. Choudum, V. Sunitha, Augmented cubes, Networks 40 (2) (2002) 71-84], is a $(2n-1)$-regular $(2n-1)$-connected graph $(n\ge 4)$. This paper determines that the 2-extra connectivity of $AQ_n$ is $6n-17$ for $n\geq 9$ and the 2-extra edge-connectivity is $6n-9$ for $n\geq 4$.
Ma, Meijie, Song, Yaxing, Xu, Jun-Ming
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Edge-fault-tolerant hamiltonicity of augmented cubes
Electronic Notes in Discrete Mathematics, 2013 Abstract The augmented cube AQ n is a hypercube Q n with additional edges between vertices that differ in a suffix. We show that AQ n with f arbitrary faulty edges contains a copy of Q n with at most n 2 n − 1 f faulty edges. This allows to transfer properties of Q n with
Kryštof Měkuta, Petr Gregor
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MetaSpace II: Object and full-body tracking for interaction and navigation in social VR
, 2015 MetaSpace II (MS2) is a social Virtual Reality (VR) system where multiple users can not only see and hear but also interact with each other, grasp and manipulate objects, walk around in space, and get tactile feedback.
Schmandt, Chris, Sra, Misha
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Homotopy Theory of Labelled Symmetric Precubical Sets
, 2014 This paper is the third paper of a series devoted to higher dimensional transition systems. The preceding paper proved the existence of a left determined model structure on the category of cubical transition systems.
Gaucher, Philippe
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Distance and Short Parallel Paths in Augmented Cubes
Electronic Notes in Discrete Mathematics, 2003 Abstract The augmented cube AQ n is recursively denned as follows: It has 2 n vertices, each labelled by an n-bit binary string a1a2… an. Define AQ 1 = K 2 . For n ≥ 2, AQ n is obtained by taking two copies AQ 0 n-l and AQ 1 n-l of AQ n-l , with vertex sets V ( AQ 0 n - l ) = {Oa 2 …a n with 1b 2 …b n iff a 2 a 3
S.A. Choudum, V. Sunitha
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A type theory for synthetic $\infty$-categories
, 2017 We propose foundations for a synthetic theory of $(\infty,1)$-categories within homotopy type theory. We axiomatize a directed interval type, then define higher simplices from it and use them to probe the internal categorical structures of arbitrary ...
Riehl, Emily, Shulman, Michael
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