Xiu-Mei Zhang, Xiao-Dong Zhang, Daniel Gray, Hua Wang
Published 2012-09-03Version 1
This paper 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 generalizes the recent results of Kirk and Wang. These trees coincide with those which were proven by Wang and independently Zhang et al. 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.
Comments: 20 pages, 2figures; Journal of graph Theory 2013
A non-$P$-stable class of degree sequences for which the swap Markov chain is rapidly mixing
Asymptotic enumeration of hypergraphs by degree sequence
Algebraic Connectivity and Degree Sequences of Trees
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