Two Topological Indices Of (Random)polycyclic Chains

The molecular graph theory of compounds has always played an extremely important role in the study of new materials.At the end of last century,with the rapid development of science and technology and the increasing of the living standards,the field of manufacturing and medicine for new materials and new drug demand grow with each passing day through a large number of chemists,the researchers presented the quantitative relationship between the various physical and chemical properties of molecules and its index value.The concept of mathematical counting polynomials was first introduced into chemistry by Polya in 1936.In 1988,the Japanese chemist Haruo Hosoya introduced the Hosoya polynomial of the distance distribution function in the graph,which can fully reflect the distance distribution in the molecular graph.The first important part of this thesis is to study the recurrence formula of Hosoya polynomials of three special polycyclic hexagonal systems.The Wiener index is one of the oldest and most studied topological indices,which was proposed by Harry,an American physical chemist,in 1947 to estimate the boiling point of paraffin.Later,it was found that the Wiener index has been widely used in the fields of organic chemistry,crystal chemistry and drug design.In this paper,the second important components is the expected value of the Wiener index in random polycyclic hexagonal systems.The text of paper main consists of three chapters,the details are as follows:In the first chapter,we first introduce the research background and development status of Hosoya polynomial and Wiener index.Secondly,some basic concepts,terms and symbols used in this paper are given.Finally,the main results of this paper are listed.In the second chapter,we give three recursive formulas for the Hosoya polynomials of the special spiro chains and Polyphenyl chain.In the third chapter,we establish exact formulas,analytical expressions and the expected values of the Wiener indices in the random spiro chains and random phenylene Chains,respectively.