On the spectral radius of weighted trees with given number of pendant vertices and a positive weight set |
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| Authors: | Shuchao Li Yi Tian |
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| Affiliation: | 1. Faculty of Mathematics and Statistics , Central China Normal University , Wuhan 430079 , China lscmath@mail.ccnu.edu.cn;3. Faculty of Mathematics and Statistics , Central China Normal University , Wuhan 430079 , China |
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| Abstract: | Let 𝒯(n,?r;?W n?1) be the set of all n-vertex weighted trees with r vertices of degree 2 and fixed positive weight set W n?1, 𝒫(n,?γ;?W n?1) the set of all n-vertex weighted trees with q pendants and fixed positive weight set W n?1, where W n?1?=?{w 1,?w 2,?…?,?w n?1} with w 1???w 2???···???w n?1?>?0. In this article, we first identify the unique weighted tree in 𝒯(n,?r;?W n?1) with the largest adjacency spectral radius. Then we characterize the unique weighted trees with the largest adjacency spectral radius in 𝒫(n,?γ;?W n?1). |
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| Keywords: | spectral radius starlike tree Perron vector weighted graph |
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