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—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.

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)

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)

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)

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)

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)