Binary codes from the line graph of the n-cube W. Fish, J.D. Key and E. Mwambene Department of Mathematics and Applied Mathematics University of the Western Cape 7535 Bellville, South Africa Abstract We examine designs and binary codes associated with the line graph of the n-cube Qn, i...
Let Qn be the n-dimensional cube represented by a graph whose vertices are sequences of 0's and 1's of length n, where two vertices are adjacent if and only if they differ only at one position. A k-dimensional subcube or a k-face of Qn is a subgraph of Qn spanned by all the...
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The k-ary n-cube, denoted by Qn k, has been one of the most common interconnection networks. In this paper, we study some topological properties of Qn k. Given two arbitrary distinct nodes x and y in Qn k, we show that there exists an x-y path of every length from [k/2]n to...
Recently Zelinka [6] proved that d(Qn), the domatic number of the n-cube, is for n equal 2p − 1 or n equal 2p, exactly 2p. We show here how d(Qn) can be determined for the preceding values, in a very simple way. We then disprove a conjecture by Zelinka and replace it by...
The Weyl group associated to a Lie algebra of type Bn and the group of graph automorphisms of the n-cube Aut(Qn) are known to be isomorphic to Z2 Sn. We provide a direct isomorphism between them via correspondence of generators. Geck and Pfeiffer have provided a parametrization of ...
The n-dimensional Mobius cube MQn is an important variant of the hypercube Qn, which possesses some properties superior to the hypercube. This paper investigates the fault-tolerant edge-pancyclicity of MQn, and shows that if MQn(n 鈮 3) contains at most n - 3 faulty vertices and/or ...
Only one comparison can be done at a time, and the comparisons are made along the n2n−1 edges of the n-cube graph Qn with vertex classes U and V. The paper deals with sequential orderings of these n2n−1 pairs(u, v) ϵU ×V for which the maximum time duration a person has...
We conjecture that the congestion of the embedding Qn3 in C3n is minimal regardless of the embedding scheme.doi:10.1016/j.yofte.2013.11.010Cui YuCollege of Computer ScienceXiaofan YangCollege of Computer ScienceLi HeCollege of Computer Science...
We investigate the structure of 3-ary n-cubes Qn3 after deleting vertices.We prove that the κ3(Qn3)=8n12 for n≥3.The previous best result by Zhu et al. about κ2(Qn3) is generalized to κ3(Qn3).doi:10.1016/j.ipl.2014.04.003Gu, Mei-Mei...