Sharif Digital Repository

There is much interest in the theoretical study of the structure of hypercubes because their structure has played an important role in the development of parallel processing and is still quite popular and influential.This thesis will begin with an introduction to hypercubes and some of their problems. Then we study the following concepts: Arboricity (The minimum number of edge-disjoint forests into which a graph can be decomposed), Galactic number (similar to arboricity but such that each component of each forest is a star), Silver coloring (Given a set I of maximal independent vertices, a silver coloring with respect to I is such that every v 2 I sees every other colors in its closed... 

Although general relativity is the underlying assumption in modern cosmology, there are still many simplifying assumptions neglecting higher order general relativistic effects. Given the precision cosmology and future surveys and the amount of data on large scales, higher order relativistic effects are to be taken into account. We will consider two categories of relativistic effects on large scale structures. First, the inhomogeneities between the source and the observer may lead to observable effects neglected so far. As future surveys will probe the universe on large scales, these effects have been the focus of recent studies. The observables being defined first, are cosmic rulers and...