The Estrada index of a graph G of n vertices is defined by E E ( G ) = ∑ i = 1 n e λ i , where λ 1 , λ 2 , ⋯ , λ n are the eigenvalues of G. In this paper, we give upper and lower bounds of E E ( G ) for almost all bipartite graphs by investigating the upper and lower bounds of the spectrum of random matrices. We also formulate an exact estimate of E E ( G ) for almost all balanced bipartite graphs.
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机译：n个顶点的图G的Estrada索引由EE（G）= ∑ i = 1 neλi定义，其中λ1，λ2，⋯，λn是G的特征值。通过研究随机矩阵谱的上限和下限，几乎所有二部图的EE（G）和下限。我们还为几乎所有平衡二部图制定了E E（G）的精确估计。
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