Research On The ISI Index And Energy

Graph theory takes graph as the research object,and converts the relationship between things into points and lines in the diagram to study the relevant nature of the figure to get the relationship between things.The topology index is a mathematical invariant derived from the molecular structure diagram of the compound.The study of energy comes from the study of chemical molecular structure,and the upper and lower bounds of index and energy are different for different graphs,so it is a popular trend to study the bounds of index and energy.The main research content of this paper is the topological index of graph based on vertex degree and its energy,analyzing the special form of index,and combining with the corresponding theoretical knowledge,giving a more accurate upper and lower bound of index and energy by scaling and proving inequality.The first chapter describes the chart's topological index,the context of graph energy research,the meaning and concepts of the graph,and describes the status quo of the ISI index and the chart's energy research.The second chapter,we use some well-known inequalities to study the upper and lower bounds of ISI index and energy of graphs.By considering the relationship between ISI index and energy and graph invariants(maximum degree,minimum degree,edge degree,etc.)and some known topological indexes,we can get some new upper and lower bounds of ISI index and energy of graphs.The third chapter,by using the basic properties of ISI-Estrada index,using the figure invariant such as the number of vertices and sides in the figure,some upper and lower bounds of the ISI-Estrada index are given,and the extremum figure is drawn.In addition,we give the bounds for ISI-Estrada index of the bipartite graph and obtain some connections between ISI-Estrada index and ISI energy.