The Fibonacci cube of dimension n, denoted as ?n, is the subgraph n-cube Qn induced by vertices with no consecutive 1’s. Ashrafi and his co-authors proved non-existence perfect codes in ?n for n ? 4. As an open problem authors suggest to consider existence generalizations cubes. most direct generalization family ?n(1s) subgraphs strings without 1s a substring where s 2 given integer. In precede...

We consider the problem of embedding the n-dimensional cube into a rectangular grid with 2n vertices in such a way as to minimize the congestion, the maximum number of edges along any point of the grid. After presenting a short solution for the cutwidth problem of the n-cube (in which the n-cube is embedded into a path), we show how to extend the results to give an exact solution for the conges...

A collection of Il 3-cube decompositions of a graph G is said to have intersection size t if there is a set S, with 181 = t, of 3-cubes which is contained in every decomposition, and no 3-cube which is not in S occurs in more than one decomposition. We determine all integers n, t and Il, with Il ::; 12, for which there exists a collection of Il 3-cube decompositions of Kn with intersection size...

In this paper we have classified the nodes of OTIS-cube based on their eccentricities. OTIS (optical transpose interconnection system) is a large scale optoelectronic computer architecture, proposed in [1], that benefit from both optical and electronic technologies. We show that radius and diameter of OTIS-Qn is n + 1 and 2n + 1 respectively. We also show that average eccentricity of OTIS-cube ...

In this paper, we prove that optimally solving an n × n × n Rubik’s Cube is NP-complete by reducing from the Hamiltonian Cycle problem in square grid graphs. This improves the previous result that optimally solving an n×n×n Rubik’s Cube with missing stickers is NP-complete. We prove this result first for the simpler case of the Rubik’s Square—an n× n× 1 generalization of the Rubik’s Cube—and th...

seismic attributes are very useful in seismic data interpretation. one of these attributes is the coherency attribute. seismic coherency is a complex trace and a geometrical attribute that is applied to a 3d cube of seismic data. it is a measure of lateral changes in acoustic impedance caused by the variation in structure, stratigraphy, lithology, porosity, and the presence of hydrocarbons. whe...

In this brief contribution, we derive an exact expression for (n 1)-cube reliability in an n-cube using a new probability fault model and M existing random fault model. Approximate results are also obtained for m-cube reliability for values of m smaller than n I . We show that the proposed probability model for computing subcube reliability is equally accurate, but computationally more efficien...

In this paper, we employ a novel approach to metarule-guided, multi-dimensional association rule mining which explores a data cube structure. We propose algorithms for metarule-guided mining: given a metarule containing p predicates, we compare mining on an n-dimensional (n-D) cube structure (where p < n) with mining on smaller multiple pdimensional cubes. In addition, we propose an efficient m...

The splitting number of a graph G consists in the smallest positive integer k 0, such that a planar graph can be obtained from G by k splitting operations, such operation replaces v by two nonadjacent vertices v1 and v2, and attaches the neighbors of v either to v1 or to v2. One of the most useful graphs in computer science is the n{cube. Dean and Richter devoted an article to proving that the ...