ON CONTAINER LENGTH AND WIDE-DIAMETER IN UNIDIRECTIONAL HYPERCUBES

Abstract

In this paper, two unidirectional binary $n$-cubes, namely, $Q_1(n)$ and $Q_2(n)$, 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 $Q_1(n)$ or in $Q_2(n)$. Furthermore,we prove that the wide-diameters of $Q_1(n)$ and $Q_2(n)$ are equal to $n+2$. At last, we show that a conjecture proposed by Jwo and Tuan is true.