On The Extremal Problems Of Two Kinds Of Topological Indices

Topological indices are a way of numeralization of molecular structure,which are obtained by performing some numerical operation on the matrix that represents the molecular graph.Topological indices are invariants of graphs,which reflect the structural character of the compound.The Szeged index and edge-Szeged index are two kinds of important topological indices in theoretical chemistry.The Zagreb indices are mainly applied in molecule design,molecule complexity and so on.They can be used to describe the molecule skeleton branch,and concerns with the molecular energy.The Zagreb indices and their reformulated forms not only are used to describe the molecule structure,but also to analyze the correlation with the characteristicsIn the thesis,we mainly study the lower bounds of the revised edge-Szeged index on the tricyclic graphs and cactus graphs,as well as the upper bounds of the reformulated Zagreb indices on two classes of graphs.The thesis can be taken partition into the following four chaptersIn Chapter 1,we firstly introduce the background and significance of topological indices.Secondly,the definitions of these topological indices we focus on are presented Moreover,the latest results on the field have been exhibited.In addition,some basic symbols and definitions of graph theory are also introduced.Finally,we present the outline the total thesis and list the results of my thesisIn Chapter 2,we show the lower bounds of the revised edge-Szeged index on tricyclic graphs and cactus graphs,respectively.Moreover,the graphs attain the bounds are characterized.In addition,we propose some problems on the field that are interestingIn Chapter 3,we obtain two upper bounds of the reformulated Zagreb indices among two kinds of graphs,which are the graphs with p pendent vertices and the graphs for which they will transform to trees by deleting one key point,respectively.Meanwhile,the graphs that meet the bounds are determined completely.Furthermore,the problems to be considered in the future are listedIn Chapter 4,we put forward ideas that can be further expanded on the above research issues.