Cayley Staining Group's Non-normality Of Order Less Than Or Equal To 4 In Cyclic Group

Based on the normalities of the Cayley graph,I give a new definition of the Cayley staining graphs' such as Cayley staining graphs' definition,concepts and properties.We study the non-normality Cayley group with order less than or equal to 4 on cyclic group,given some conclusions about it.This thesis consists of four chapters:Chapter 1:Introduces the historical background of this paper,and briefly summarizes the content structure of this paper and give research project.Chapter 2:Some basic concepts and related properties are given in this paper,such as group's concept,the non-normality of Cayley group and so on.To prepare for the results of Cayley staining graph.Chapter 3:Firstly,Given the definition of Cayley staining graph,extend Cayley graphs' concept.Study some basic concept and properties of Cayley staining graph.Then,we introduce and prove the Cayley-n staining graphs'non-normality.Chapter 4:Given some examples of the Chapter 3's Cayley-n staining graphs' conclusion.Main about studying the non-normality group with order less or equal to 4 on a cyclic Cayley group,and give the necessary condition.