Wiener Index of Trees

• Main Authors: Liu,Yi Hui, 劉懿慧
• Other Authors: Shaw,Hong-Min
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/sqdfv8

碩士 === 輔仁大學 === 數學系研究所 === 99 === The purpose of this thesis is to compare the Wiener indices of different trees. A well- known classical result is that among all the n-vertex trees, the Wiener index of the path is the maximum and the Wiener index of the star is minimum. In this thesis we provide another proof of it based on a ”local-transfer” approach. Next we consider tree (k1, k2, k3), a tree consisting of three edge-disjoint paths of k1, k2 and k3 vertices which share one same end vertex. We compute the Wiener index of tree (k1, k2, k3) directly and we find that there is a relation between the Wiener index of (k1, k2, k3) and the product k1k2k3; however this result is already known. Furthermore we consider trees of maximum degree 3 and with exactly two vertices of degree 3. We characterize trees with maximum and minimum Wiener indices. Finally we consider all trees of maximum degree 3. Although we have not characterized trees with maximum and minimum Wiener indices yet, we found that W( bT) = 4W(T) + [2n(T) + 1]2, where T is a (k1, k2, k3) and bT is a tree obtained from T so that the degree of each vertex is either 3 or 1.