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- Frank K. Hwang, Sheng-Chyang Liaw
- IEEE/ACM Trans. Netw.
- 2000

—We give necessary and sufficient conditions for strictly nonblocking three-stage Clos networks with two types of multicast traffic. Then, we extend the results to other models where the routing is under certain restrictions. Finally, we compare our results with existing literature to mark the differences and similarities.

- Sheng-Chyang Liaw, Gerard J. Chang
- J. Comb. Optim.
- 1998

Reliability and efficiency are important criteria in the design of interconnection networks. Recently, the w-wide diameter d w (G), the (w − 1)-fault diameter D w (G), and the w-Rabin number r w (G) have been used to measure network reliability and efficiency. In this paper, we study d w (G), D w (G) and r w (G) using the strong w-Rabin number r * w (G) for… (More)

- Gerard J. Chang, Sheng-Chyang Liaw
- Ars Comb.
- 2003

Reliability and efficiency are important criteria in the design of interconnection networks. Recently, the w-wide diameter d w (G), the (w − 1)-fault diameter D w (G), and the w-Rabin number r w (G) have been used to measure network reliability and efficiency. In this paper, we study wide diameters for an important class of parallel networks— butterfly… (More)

- Gerard J. Chang, Jer-Jeong Chen, David Kuo, Sheng-Chyang Liaw
- Discrete Applied Mathematics
- 2007

For positive integers j ≥ k, an L(j, k)-labeling of a digraph D is a function f from V (D) into the set of nonnegative integers such that |f (x) − f (y)| ≥ j if x is adjacent to y in D and |f (x) − f (y)| ≥ k if x is of distant two to y in D. Elements of the image of f are called labels. The L(j, k)-labeling problem is to determine the λ j,k-number λ j,k… (More)

- Frank K. Hwang, Sheng-Chyang Liaw, Li-Da Tong
- IEEE Trans. Communications
- 2003

Kreweras considered the problem of counting noncrossing partitions of the set {1, 2, · · · , n}, whose elements are arranged into a cycle in its natural order, into p parts of given sizes n 1 , n 2 , · · · , np (but not specifying which part gets which size). He gave a beautiful and surprising result whose proof resorts to a recurrence relation. In this… (More)

- Sheng-Chyang Liaw, Gerard J. Chang
- Discrete Mathematics
- 1999

- Gerard J. Chang, Sheng-Chyang Liaw, Hong-Gwa Yeh
- Discrete Applied Mathematics
- 2002

For a positive integer k, a k-subdominating function of a graph G = (V; E) is a function f : V → {−1; 1} such that u∈N G [v] f(u) ¿ 1 for at least k vertices v of G. The k-subdomination number of G, denoted by ks (G), is the minimum of v∈V f(v) taken over all k-subdominating functions f of G. In this article, we prove a conjecture for k-subdomination on… (More)

- Fei-Huang Chang, Ma-Lian Chia, David Kuo, Sheng-Chyang Liaw, Jen-Chun Ling
- Theor. Comput. Sci.
- 2016