| Graph theory is a new and rapidly developing discipline.It has many links with computer,chemistry,physics and so on.It has attracted the attention of many scholars at home and abroad.This paper mianly determines the extremum of the non-peripheral Wiener index of trees.The main contents are divided into the following three parts:Firstly,the second chapter determines maximum and minimum non-peripheral Wiener index of trees with order and the number of peripheral vertices,and depicts the structure of the tree corresponding to the maximum or minimum.Sceondly,the third chapter determines minimum of the non-peripheral Wiener index of trees with order and matching number,and depicts the structure of the tree corresponding to the minimum.Finally,the fourth chapter determines maximum of the non-peripheral Wiener index of trees with order and fixed maximum degree,depicts the structure of the tree corresponding to the maximum,and obtains some properties of this kind of tree corresponding to the minimum. |
