Wiener Index of Trees
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 an...
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ndltd-TW-100FJU004790142019-05-15T20:43:20Z http://ndltd.ncl.edu.tw/handle/sqdfv8 Wiener Index of Trees 樹的Wiener Index Liu,Yi Hui 劉懿慧 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. Shaw,Hong-Min 蕭鴻銘 2009 學位論文 ; thesis 26 zh-TW |
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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.
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author2 |
Shaw,Hong-Min |
author_facet |
Shaw,Hong-Min Liu,Yi Hui 劉懿慧 |
author |
Liu,Yi Hui 劉懿慧 |
spellingShingle |
Liu,Yi Hui 劉懿慧 Wiener Index of Trees |
author_sort |
Liu,Yi Hui |
title |
Wiener Index of Trees |
title_short |
Wiener Index of Trees |
title_full |
Wiener Index of Trees |
title_fullStr |
Wiener Index of Trees |
title_full_unstemmed |
Wiener Index of Trees |
title_sort |
wiener index of trees |
publishDate |
2009 |
url |
http://ndltd.ncl.edu.tw/handle/sqdfv8 |
work_keys_str_mv |
AT liuyihui wienerindexoftrees AT liúyìhuì wienerindexoftrees AT liuyihui shùdewienerindex AT liúyìhuì shùdewienerindex |
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1719104292216897536 |