New relationship between Energy and Estrada Index - Li, Yalan; Deng, Bo; Ye, Chengfu (Discontinuity, Nonlinearity, and Complexity, 2026)
Let $G$ be a graph on $n$ vertices, and let $λ_{1}, …,λ_{n}$ 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 $EE(G)=\sum ^{n} _{i=1}e^{λ_{i}}$. We get some new bounds for $EE(G)$. Some special inequalities are used to obtain the relationship between $E(G)$ and $EE(G)$.