Relevant Research On Topological Indices Multiplicative Zagreb

Topological indices of graphs based on the degree is a hot topic in the research of Graph Theory.It not only has essentical theoretical significance,but also en-joys practical applications in computer science,medicine,quantum computation and chemistry.In the simple connected graph G,the first multiplicative Zagreb index ?1 is considered to be the product of square of the degree of its vertices,while the second multiplicative Zagreb index ?2 is expressed as the product of end vertex degree of each over all edges.At the same time,Zagreb index is one of the most popular and widely used structural indicators based on molecular graph.It can not only effec-tively describe the branching degree of organic molecules,but also be widely used to predict the physical and chemical properties and biological activities of organic compounds.In this paper,we mainly study the related problems of topological index Multiplicative Zagreb by using the techniques of structural graph theory.This thesis consists of five chapters,the main content as follows:In Chapter 1,we introduce the background and significance of the research,including the development of mathematicians of a representative domestic and over-seas regarding this aspect in recent years.Based on this research background and profound discussion on the status quo,it fully shows the main work's necessity and innovation.In Chapter 2,we mainly give some symbols and basic definitions that we needed in this paper.In Chapter 3,we focus on the extremal multiplicative Zagreb indices of trees with given number of vertices of maximum degree.In the first subsection,we first discuss the bounds of the first multiplicative Zagreb index in the class of the tree Tn,k with given number of vertices of maximum degree,in addition,we give the corresponding extremal graphs.In the second subsection,we explore the bounds of the second multiplicative Zagreb index.Moreover,the structure of the extremal graphs are provided when they arrive the upper and lower bounds,respectively.In Chapter 4,we study the bounds of the first and second multiplicative Zagreb index of graphs subject to given number of cut edges in the class of Gn,k.Furthermore,the extremal graphs are given.In Chapter 5,we summarize the main results in this paper and give some prospects for further research in the future.