Hypercubes and Some of their Problems

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Karisani, Negin | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43245 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahmoodian, Ebadollah
Abstract:
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 neighbourhood).There is a lot of conjectures and problems in these concepts and we answer some of them
Keywords:
Graphs ; Decomposition ; Network ; Hypercube ; Arboricity ; Galactic Number ; Silver Coloring