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... 

Since today graphs have many applications in different sciences including computer networks, in this thesis a number of graphs which have been widely used in computer networks, are studied.The graphs presented in this thesis are hypercubes, generalized hypercubes (Bhuyan and grawal, 1984), balanced hypercubes (Huang and Jie, 1992) and the star graphs (Sheldon and Akers, 1987), which are the generalization of the hypercubes and have similar properties.In general the graph which is considered for computer networks as an interconnection structure,should have small degrees of vertices, a small diameter, and a large number of paths between any two vertices. Thus in our studies these three...