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.
The Number of Subtrees of Trees with Given Degree Sequence
Article first published online: 6 AUG 2012
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 73, Issue 3, pages 280–295, July 2013
How to Cite
Zhang, X.-M., Zhang, X.-D., Gray, D. and Wang, H. (2013), The Number of Subtrees of Trees with Given Degree Sequence. J. Graph Theory, 73: 280–295. doi: 10.1002/jgt.21674
- Issue published online: 10 MAY 2013
- Article first published online: 6 AUG 2012
- Manuscript Revised: 20 APR 2012
- Manuscript Received: 2 MAR 2011
- National Natural Science Foundation of China. Grant Number: 10971137
- National Basic Research Program (973) of China. Grant Number: 2006CB805900
- Science and Technology Commission of Shanghai Municipality (STCSM). Grant Number: 09XD1402500
- 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 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.