Abstract
This article introduces a new variant of hypercubes Hn. The n-dimensional twisted hypercube Hn is obtained from two copies of the (n−1)-dimensional twisted hypercube Hn−1 by adding a perfect matching between the vertices of these two copies of Hn−1. We prove that the n-dimensional twisted hypercube Hn has diameter (1+o(1))n/log2n. This improves on the previous known variants of hypercube of dimension n and is optimal up to an error of order o(n/log2n). Another type of hypercube variant Zn,k that has similar structure and properties as Hn is also discussed in the last section.
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