Laplacian Estrada index of trees

Details Laplacian Estrada index of trees Laplacian Estrada index of trees

2011-06-15

arxiv.org/abs/1106.3041v1

MATCH Commun. Math. Comput. Chem. 63 (2010), 769-776

Mathematics

Combinatorics

8 pages, 1 figure

Scientific paper

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 $LEE (G) = \sum\limits_{i = 1}^n e^{\mu_i}$. 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.

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