Research On The Domination Number Of Generalized Petersen Graphs P(n,5)

In recent years,the domination theory of graphs and some of the topics related to the colouring,total domination,have been a relatively active area of research in the graph theory.The research on the domination theory of graphs not only has important theoretical significance,provides necessary theoretical basis to research on the graph theory in the future,but also has a wide range of applications in the design and analysis,traffic routes of communication network optimization theory,social science,compu-tational complexity and design,etc.However,due to confirming a graph domination NP-completely,now only a few domination numbers of graphs have been get a good research.This paper mainly studies the domination number of generalized Petersen and re-lated eccentric distance of the tree given domination number.The article contains four chapters.In the first chapter,the paper summarizes the research background and research progress about domination number of graphs,and introduces some basic concepts of graph theory,domination theory,the eccentric distance and the preparatory knowledge,lays a theoretical foundation for the later research,and introduces the main job of this article.In the second chapter,the paper researches the domination number of generalized Petersen graph P(n,5).Being main part of this chapter in this article,it uses the re-searching methods about the upper bound of the domination number of P(c · 5,5)(c ? 4)and P(n,4),divides domination number of P(n,5)(n ? 20),deduces a better upper bound of domination number of P(n,5)(n ? 20)according to n = 5c,5c + 1,5c + 2,5c +3,5c + 4(c ? 0,1,2,3(/mod4)),and finds the upper bound of the domination number P(n,5)(n ?11)accordingly.In the third chapter,the paper researches the largest eccentric distance sum of the tree given domination number of five.Useing research methods of the largest eccentric distance sum of trees given domination number of four,it deduces the largest eccentric distance sum of the tree given domination number of five.By using the method of dis-proof analysis and argument on different structure trees,it can proof to the conclusion.In the fourth chapter,the paper is about summary and outlook.It summarizes the main conclusions of this paper and hope to expand and promote the related knowledges of domination number in the future,which apply in the practical fields.