Research On Algebraic Index Problem Of Probability Graph

Graph theory is an important branch of applied mathematics.It is closely related to other mathematical branches and can describe complex mathematical models,so it involves many disciplines.Therefore,it also has a wide application background.The distance based topological indicators in graph theory are closely related to the topological indicators related to chemical molecules.Some distance topological indicators in graph theory can be applied to the discipline of chemistry and a database of specified topological indicator values can be established.Molecular topological index is a way to digitize molecular structure,which is applied in the field of chemistry.It is a collision between mathematics and chemistry,and many topological indices are closely related to the physical and chemical properties of chemical substances.The algebraic index is used to calculate the correlation,and the molecular graph is used to express the structure of the compound molecule,and then the molecular structural properties are discussed.Deep research on topological indices can better understand molecular diagrams and solve some chemical problems using convenient mathematical methods.In this paper,we mainly discuss two types of molecular diagrams.One is a cyclooctetraene chain with n octagons.Its four structures are formed by cutting edges gradually adjacent to octagons.There are4^n-（²n≥3）different adjacencies.The other is a helical chain with n octagons.Its four structures are directly and gradually adjacent to octagons.The connection points are called cut points.There are also4^n-（²n≥3）different adjacencies.The main content of this article is to calculate the expected value of algebraic indicators through the sum of recursive relationships,and calculate the extreme and the average value according to the probability problem.The main contents include:The first chapter introduces the research background and the research status at home and abroad.The second chapter introduces six algebraic indicators and two probability graphs.The third chapter calculates the expected and extreme values of Wiener index,Gutman index,and Schultz index in different probability graphs.The fourth chapter calculates the expected value and extreme value of Kirchhoff index,multiplication-Kirchhoff index and additivity-Kirchhoff index in different probability graphs.The fifth chapter calculates the average value of six algebraic indicators in different probability graphs.Figure[4]Reference[94]...