Let T(n) denote the number of n-simplices in a minimum cardinality decomposition of the n-cube into n-simplices. For n 1 we show that T(n) H(n), where H(n) is the ratio of the hyperbolic volume of the ideal cube to the ideal regular simplex. H(n) 1 2 6 n=2 (n+1) ? n+1 2 n!. Also lim n!1 p nH(n)] 1=n 0:9281. Explicit bounds for T(n) are tabulated for n 10, and we mention some other results on hy...

In this dissertation, we investigate fault-tolerant capabilities of the k-ary n-cubes with respect to the hamiltonian and hamiltonian connected properties. The k-ary n-cube is a bipartite graph if and only if k is an even integer. Let F be a faulty set with nodes and/or links, and let k ≥ 3 be an odd integer. When |F | ≤ 2n − 2, we show that there exists a hamiltonian cycle in a wounded k-ary n...

The Fibonacci cube [6] is a new class of graphs that are inspired by the famous numbers. Because of the rich properties of the Fibonacci numbers [1], the graph also shows interesting properties. For a graph with AT nodes, it is known [6] that the diameter, the edge connectivity, and the node connectivity of the Fibonacci cube are in the order of 0(log N), which are similar to the Boolean cube (...

The paper approaches the classical combinatorial problem of freeness of words, in the more general case of partial words. First, we propose an algorithm that tests efficiently whether a partial word is kfree or not. Then, we show that there exist arbitrarily many cube-free infinite partial words containing an infinite number of holes, over binary alphabets; thus, there exist arbitrarily many k-...

In this study some algebraic transformations on hypercube system are proposed. The presented transformations of forbidden subcubes provide defining set of all maximal and nonfaulty subcubes, and subset of minimal and nonfaulty subcubes included certain given vertices. It provides formal and simple findingsof all the current sources and targets of information, and also the pathways between them....

We discuss multicasting for the n-cube network and its close variants, the Chord and the Binomial Graph (BNG) Network. We present simple transformations and proofs that establish that the sp-multicast (shortest path) and Steiner tree problems for the n-cube, Chord and the BNG network are NP-Complete.