Two Class Of Spiders With Minimal Total π-electron Energy

The structure of compounds usually use polygon to show, called the molec-ular diagram of compound. Research shows that the experimental heats fromthe formation of conjugated compounds are closely related to the totalπ-electron energy. In fact, it is often repeated claim that the HMO totalπ-electron energies are in good agreement with experimental enthalpies of therespective conjugated compounds. And then we always calculate it to get theenergies of compounds molecules.The totalπ-electron energy of compounds molecules is a bridge betweenthe chemical structure and its thermodynamic stability, furthermore, study oftotalπ-electron energies of chemical graph is of both the profound theoreti-cal and practical significance. In this paper, we mainly study two classes ofcycloparafin hydrocarbon with branches, we found six-membered ring spirospiders with the minimal totalπ-electron energy and polyphenyl spiders withthe minimal totalπ-electron energy. It has important significance for Molecu-lar structure and chemical properties of subclass of cycloparafin hydrocarbonwhich are spiro-compound and biphenyl compounds in theoretical chemistry.In chapter 1, we introduce the background of our study and some notations,and recall study of the totalπ-electron energy. In chapter 2, we study theminimal totalπ-electron energy of polyphenyl spiders with given length ofeach leg, furthermore, by transformation, we can get the minimal totalπ-electron energy of polyphenyl spiders with given numbers of benzene rings. Inchapter 3, we study the minimal totalπ-electron energy of six-membered ringspiro spiders with given length of each leg, furthermore, by transformation, wecan get the minimal totalπ-electron energy of six-membered ring spiro spiderswith given numbers of six-membered rings.In this paper, comparing coe?cients of characteristic polynomial of twobipartite graphs and using transformation of graphs are the key for our argu- mentation. The main method for proving our results is by contradiction andinduction.