Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class has been studied extensively and generalized in many different directions. Induced on with restricted runlengths as vertices define Fibonacci-run graphs. These have same number cubes, but fewer edges graph theoretical properties...

Among the classical models for interconnection networks are hypercubes and Fibonacci cubes. cubes induced subgraphs of obtained by restricting vertex set to those binary strings which do not contain consecutive 1s, counted numbers. Another numbers with a restriction on runlengths. Induced hypercube latter as vertices define Fibonacci-run graphs. They have same number cubes, but fewer edges diff...

A Fibonacci string is a length n binary string containing no two consecutive 1s. Fibonacci cubes (FC), Extended Fibonacci cubes (ELC) and Lucas cubes (LC) are subgraphs of hypercube defined in terms of Fibonacci strings. All these cubes were introduced in the last ten years as models for interconnection networks and shown that their network topology posseses many interesting properties that are...

We provide explicit formulas for the maximum number qk(n) of disjoint subgraphs isomorphic to the k-dimensional hypercube in the n-dimensional Fibonacci cube Γn for small k, and prove that the limit of the ratio of such cubes to the number of vertices in Γn is 1 2k for arbitrary k. This settles a conjecture of Gravier, Mollard, Špacapan and Zemljič about the limiting behavior of qk(n).

The Fibonacci cube Γn is the subgraph of the hypercube induced by the binary strings that contain no two consecutive 1’s. The Lucas cube Λn is obtained 5 from Γn by removing vertices that start and end with 1. We characterize maximal induced hypercubes in Γn and Λn and deduce for any p ≤ n the number of maximal p-dimensional hypercubes in these graphs.

The generation of uniform pseudo-random numbers between 0 and 1 is important in many numerical simulations. The purpose of this report is to explore the best generator(s) of such random numbers in terms of statistical properties and speed. While attempting to find the best generator in general, the specific goal of this report is to find the best generator for Latin hypercube sampling [Iman and...

Fibonacci Cubes (FCs), together with the enhanced and extended forms, are a family of interconnection topologies formed by diluting links from binary hypercube. While they scale up more slowly, they provide more choices of network size. Despite sparser connectivity, they allow efficient emulation of many other topologies. However, there is no existing fault-tolerant routing strategy for FCs or ...

A Fibonacci string of order n is a binary string of length n with no two consecutive ones. The Fibonacci cube n is the subgraph of the hypercube Qn induced by the set of Fibonacci strings of order n. For positive integers i; n, with n¿ i, the ith extended Fibonacci cube is the vertex induced subgraph of Qn for which V ( i n) = V i n is de2ned recursively by V i n+2 = 0V i n+1 + 10V i n; with in...

Embeddings of various graph classes into hypercubes have been widely studied. Almost all these classes are regularly structured graphs such as meshes, complete trees or pyramids. In this paper, we present a general method for one-to-one embeddings of irregularly structured graphs into their optimal hypercubes, based on extended edge bisectors of graphs. An extended edge bisector is an edge bise...