The Number of Subtrees of Trees with Given Degree Sequence |
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| Authors: | Xiu‐Mei Zhang Xiao‐Dong Zhang Daniel Gray Hua Wang |
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| Institution: | 1. DEPARTMENT OF MATHEMATICS, SHANGHAI JIAO TONG UNIVERSITY, , SHANGHAI, 200240 P. R. CHINA;2. DEPARTMENT OF MATHEMATICS, SHANGHAI SANDAU UNIVERSITY, , SHANGHAI, 201209 P. R. CHINA;3. DEPARTMENT OF MATHEMATICS, UNIVERSITY OF FLORIDA GAINESVILLE, , FLORIDA, 32611;4. DEPARTMENT OF MATHEMATICAL SCIENCES, GEORGIA SOUTHERN UNIVERSITY STATEBORO, , GEORGIA, 30460 |
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| Abstract: | 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. |
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| Keywords: | tree subtree degree sequence majorization 05C05 05C30 |
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