Abstract
Let \(G\) be a \(n\)-vertex simple graph. Suppose \(A(G)\) and \(L(G)= \Delta (G) - A(G)\) are adjacency and Laplacian matrix of \(G\), respectively, where \(\Delta(G)\) is degree matrix of \(G\). \(EE(G) =\sum_{i=1}^ne^{\lambda_i}\) and \(LEE(G)=\sum_{i=1}^ne^{\mu_i}\) are called Estrada and Laplacian Estrada index of \(G\), where \(\lambda_i\) and \(\mu_i\), \(1\leq i \leq n\), denote the eigenvalues of \(A(G)\) and \(L(G)\). In this paper, some new upper and lower bounds for \(EE(G)\) and \(LEE(G)\) are given. Moreover, some relations between \(EE(G)\) and \(LEE(G)\), and the number of spanning trees are established.
