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Laplacian Estrada index of trees | | Aleksandar Ilic
; Bo Zhou
; | | Date: |
15 Jun 2011 | | Abstract: | Let $G$ be a simple graph with $n$ vertices and let $mu_1 geqslant mu_2
geqslant...geqslant mu_{n - 1} geqslant mu_n = 0$ be the eigenvalues of
its Laplacian matrix. The Laplacian Estrada index of a graph $G$ is defined as
$LEE (G) = sumlimits_{i = 1}^n e^{mu_i}$. Using the recent connection
between Estrada index of a line graph and Laplacian Estrada index, we prove
that the path $P_n$ has minimal, while the star $S_n$ has maximal $LEE$ among
trees on $n$ vertices. In addition, we find the unique tree with the second
maximal Laplacian Estrada index. | | Source: | arXiv, 1106.3041 | | Services: | Forum | Review | PDF | Favorites | |
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