Study On The Domination Parameters Of Graph

The research of graph domination parameter theory is one of the main directions of graph theory.For example,"facility location" problem,equipment placement problem and other practical problems can be attributed to the domination parameters of graph to solve.The main research content of tjis paper is as follows:In the first chapter,we mainly introduce the background and significance of the theoretical research on the domination parameters of graphs,give the basic concepts and symbols required in this paper,and introduce the work done in this paper.In the second chapter,we mainly characterizes the tree with domination number? and the maximal eccentric distance sum.Some know results have been extended.In the third chapter,we mainly characterize the connected graphs G for which?h(G)=?(G),which solved an open question posed by Michael A.Henning et al.[1].we also characterize the tree for which ?h(G)=?(G).In the fourth chapter,we establish a new upper bound on the double Roman domination number of a tree and characterize the trees attaining the upper bound.We obtain an upper bound on the double Roman domination number of a graph in terms of its order and domination number.This result improves existing known results.In the fifth chapter,we summarize the main conclusions of this paper and look forward to the future research.