| The hyper-Wiener index is one of the distance-based graph invariants.It can be used to predict some physicochemical properties of organic compounds.In this paper,by the properties of hyper-Wiener index,according to the specific characteristics of the corresponding diameters of trees,we determining the maximum and the maximal graph classes of hyper-Wiener index of trees with fixed diameters by graph transformation,and the corresponding extreme values are obtained.In chapter 1,we introduce the research background and the related concept on graph theory and hyper-Wiener index.We briefly state the research status and progress of hyper-Wiener index.Finally,the main results of this thesis are given.In chapter 2,we concentrate on which maximize the hyper-Wiener index among all trees with given order and specific diameter at most 5.For the diameter of 3 and 4,according to the graphic feature,we use the graphic transformation or the function to obtain the corresponding maximum graph classes;For the diameter of 5,on the premise of the same central point degree,the corresponding maximal graph classes are obtained.In the maximal graph classes,the maximum value corresponding to the specific order is given by Matlab software.At last,according to the obtained conclusions,conjectures are made on the maximal graph classes of hyper-Wiener index for trees with diameters of 5 and 6 respectively. |
