Research On Domination Number Of Several Classes Of Graphs

Graph theory is a very valuable subject,which takes graph as its research object,expresses things with vertexes,relations between things with edges,to probe into the relations between things.In recent years,graph theory is a very important and rapidly developing branch of mathematics,and the domination number theory of graph is a very important part of studying graph theory.The research on the domination number theory of graphs helps us to solve a lot of practical problems in life,such as the placement of rescue equipment,Social network and other problems.In this paper,we do theoretical research on the domination parameters of graphs,and give the exact value of one domination number of several classes of graphs.In the first chapter,we introduce the origin and development of graph theory,the research background and significance of this paper,and some basic concepts and symbolic representations.In the second chapter,based on the upper bound and lower bound of the 2-domination number of the generalized Petersen graph P(n,3)(where n=5k+1,5k+2,5k+3)given by D.Bakhshesh et al.,we give the exact value of the 2-domination number of the generalized Petersen graph.In the third chapter,we study the relation between the vertex cover of a graph and the domination number of a central graph,and give the equality relation between the vertex cover of a tree T and the domination number of a central graph.In the fourth chapter,we discuss the 2-domination number and 3-domination number of the central graph of general graphs and the k-domination number of the central graphs of several special graphs.In the fifth chapter,we make a systematic summary of the results of this paper and look forward to the future research work.