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The asymptotic number of occurrences of a subtree in trees with bounded maximum degree and an application to the Estrada index | Xueliang LI
; Yiyang Li
; | Date: |
7 May 2010 | Abstract: | Let $mathcal {T}^{Delta}_n$ denote the set of trees of order $n$, in which
the degree of each vertex is bounded by some integer $Delta$. Suppose that
every tree in $mathcal {T}^{Delta}_n$ is equally likely. For any given
subtree $H$, we show that the number of occurrences of $H$ in trees of
$mathcal {T}^{Delta}_n$ is with mean $(mu_H+o(1))n$ and variance
$(sigma_H+o(1))n$, where $mu_H$, $sigma_H$ are some constants. As an
application, we estimate the value of the Estrada index $EE$ for almost all
trees in $mathcal {T}^{Delta}_n$, and give an explanation in theory to the
approximate linear correlation between $EE$ and the first Zagreb index obtained
by quantitative analysis. | Source: | arXiv, 1005.1135 | Services: | Forum | Review | PDF | Favorites |
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