The Number of Subtrees of Trees with Given Degree Sequence

This article investigates some properties of the number of subtrees of a tree with given degree sequence. These results are used to characterize trees with the given degree sequence that have the largest number of subtrees, which generalize the recent results of Kirk and Wang (SIAM J Discrete Math 2...

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Bibliographic Details
Published inJournal of graph theory Vol. 73; no. 3; pp. 280 - 295
Main Authors Zhang, Xiu-Mei, Zhang, Xiao-Dong, Gray, Daniel, Wang, Hua
Format Journal Article
LanguageEnglish
Published Hoboken Blackwell Publishing Ltd 01.07.2013
Wiley Subscription Services, Inc
Subjects
05C05
05C30
degree sequence
majorization
Studies
subtree
tree
Trees
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Summary:This article investigates some properties of the number of subtrees of a tree with given degree sequence. These results are used to characterize trees with the given degree sequence that have the largest number of subtrees, which generalize the recent results of Kirk and Wang (SIAM J Discrete Math 22 (2008), 985–995). These trees coincide with those which were proven by Wang and independently Zhang et al. (2008) to minimize the Wiener index. We also provide a partial ordering of the extremal trees with different degree sequences, some extremal results follow as corollaries.
Bibliography:National Basic Research Program (973) of China - No. 2006CB805900
istex:C649D1AE26B3C0B62FF632E6A3503F786D6EEE1B
ark:/67375/WNG-4HDZSNJ0-G
National Natural Science Foundation of China - No. 10971137
ArticleID:JGT21674
Science and Technology Commission of Shanghai Municipality (STCSM) - No. 09XD1402500
Contract grant sponsor: National Natural Science Foundation of China; Contract grant number: 10971137; Contract grant sponsor: the National Basic Research Program (973) of China; Contract grant number: 2006CB805900; Contract grant sponsor: Science and Technology Commission of Shanghai Municipality (STCSM); Contract grant number: 09XD1402500.
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.21674