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The Number of Subtrees of Trees with Given Degree Sequence


  • 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.


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.