Though embedding problems have been considered for several regular graphs, it is still an open problem for hypercube into torus. In the paper, we prove the conjecture mathematically and obtain the minimum wirelength of embedding for hypercube into Cartesian product of paths and/or cycles. In addition, we explain that Gray code embedding is an optimal strategy in such embedding problems.

翻译：尽管嵌入问题已在若干正则图中得到研究，但超立方体到环面的嵌入仍是一个未解决问题。本文从数学上证明了该猜想，并获得了超立方体嵌入到路径和/或环的笛卡尔积时的最小线长。此外，我们阐释了格雷码嵌入在此类嵌入问题中是一种最优策略。