Let $G$ be a graph on $n$ vertices and ${\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n$ its eigenvalues. The Estrada index of $G$ is an invariant that is calculated from the eigenvalues of the adjacency matrix of a graph. In this paper, we present some new lower bounds for the Estrada index of graphs and in particular of bipartite graphs that only depend on the number of vertices, the number of edges, Randić index, maximum and minimum degree and diameter.

中文翻译：

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Estrada指数的下限

让 $G$ 成为图 $ñ$ 顶点和 ${\lambda }_{\mathrm{1个}}，{\lambda }_2，\dots ，{\lambda }_{ñ}$它的特征值 的Estrada指数$G$是根据图的邻接矩阵的特征值计算出的不变量。在本文中，我们为图的Estrada索引（尤其是二部图）提出了一些新的下界，这些下界仅取决于顶点数，边数，Randić指数，最大和最小度数和直径。