On maximum Estrada indices of bipartite graphs with some given   parameters
  The Estrada index of a graph $G$ is defined as $EE(G)=\sum_{i=1}^ne^{\lambda_i}$, where $\lambda_1,$ $ \lambda_2,\ldots, \lambda_n$ are the eigenvalues of the adjacency matrix of $G$. In this paper, we characterize the unique bipartite graph with maximum Estrada index among bipartite graphs with given matching number and given vertex-connectivity, edge-connectivity, respectively. 
Fei Huang, Xueliang Li, Shujing Wang
math.CO