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Discontinuity, Nonlinearity, and Complexity 10(4) (2021) 617--623 | DOI:10.5890/DNC.2021.12.003

Yalan Li$^1$, Bo Deng$^{2}$ , Chengfu Ye$^{2}$

$^1$ School of Computer, Qinghai Normal University, Xining 810001, China

$^{2}$ School of Mathematics and Statistics, Qinghai Normal University, Xining 810001, China

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Abstract

Let $G$ be a graph on $n$ vertices, and let $\lambda_{1}, \cdots,\lambda_{n}$ be its eigenvalues. The energy $E(G)$ of a graph $G$ is defined as the sum of absolute values of the eigenvalues of $G$. The Estrada index of the graph $G$ is defined as $EE(G)=\sum ^{n} _{i=1}e^{\lambda_{i}}$. We get some new bounds for $EE(G)$. Some special inequalities are used to obtain the relationship between $E(G)$ and $EE(G)$.

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