On container length and wide-diameter in unidirectional hypercubes

In this paper, two unidirectional binary n-cubes, namely, Q₁ (n) and Q₂H, proposed as high-speed networking schemes by Chou and Du, are studied. We show that the smallest possible length for any maximum fault-tolerant container from a to b is at most n + 2 whether a and b are in Q₁ (n) or in Q₂(n). Furthermore, we prove that the wide-diameters of Q₁(n) and Q₂(n) are equal to n + 2. At last, we show that a conjecture proposed by Jwo and Tuan is true.