Ordering Trees By Their Degree Distance

The degree distance is the sum of the product of all pairs of a (connected) graph and itsdegree.It is one of the important topological in Chemistry since Dobrynin,Kochetova andGutman defined it in their paper in1994. It is used for the structure of molecule, after manyyears’ reaseach, scientists found that there is a very close relation between the physicalchemicalproperties and biological activity of many compounds. After several years, Mathematicianbegan to pay attention to this index and discribed it in Mathemarical words. This kind oftopological indices include the Wiener index. And Wiener index get a widely reasearch.In this paper, I make a research of trees on basis of the existing results. He. determinedthese trees that from the fifth to the twelfth trees according to the descending order in this orderand the corresponding degree distance. Chang. And He. characterized these trees that from thefifth to the twentieth trees according to the ascending order in this order and the correspondingdegree distance. In this paper, problem on the ordering trees of which steps are n by theirdegree distance is investigated with graph transformation and the recursive caculation, and fromthe fifth to the tirteenth trees in the descending order and from the fifth to the twentieth treesaccording to the ascending order and the corresponding degree distance of these trees aredetermined.