Taiwanese Journal of Mathematics

ON CONTAINER LENGTH AND WIDE-DIAMETER IN UNIDIRECTIONAL HYPERCUBES

Changhong Lu and Kemin Zhang

Full-text: Open access

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.

Article information

Source
Taiwanese J. Math., Volume 6, Number 1 (2002), 75-87.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407401

Digital Object Identifier
doi:10.11650/twjm/1500407401

Mathematical Reviews number (MathSciNet)
MR1884456

Zentralblatt MATH identifier
0999.05066

Subjects
Primary: 05C40: Connectivity 68M10: Network design and communication [See also 68R10, 90B18] 68R10: Graph theory (including graph drawing) [See also 05Cxx, 90B10, 90B35, 90C35]

Keywords
hypercube wide-diameter container connectivity

Citation

Lu, Changhong; Zhang, Kemin. ON CONTAINER LENGTH AND WIDE-DIAMETER IN UNIDIRECTIONAL HYPERCUBES. Taiwanese J. Math. 6 (2002), no. 1, 75--87. doi:10.11650/twjm/1500407401. https://projecteuclid.org/euclid.twjm/1500407401


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