Abstarct: A great deal of attention has been paid to spectral graphs in recent years because spectral graphs play an important role in discovering the structure of graphs. The set of eigenvalue of graphs is named spectral graph. This subject is a part of algebraic theory of graphs and is more related to linear and matrix algebra theoretically. The theory of spectral graphs has applications in discovering the structure of graphs as well as other sciences such as chemistry, physics, electrical engineering, development and computer. In this thesis, it has been attempted to study the subjects related to spectral graphs, and to examine their application in computer science. In the first chapter, definitions and elementary concepts are dealt. In the second chapter, spectral characteristics of graphs and bounds of spectral sets are examined. In the third chapter, applications of spectral graphs in the subject of spectral embedding of graphs are examined. In the fourth chapter, application of spectral graph in the question of analysis principal components is examined. In the fifth chapter, application of spectral graph in face recognizing is examined.