Some properties on Estrada index of folded hypercubes networks (Q1722236)

Summary: Let \(G\) be a simple graph with \(n\) vertices and let \(\lambda_1, \lambda_2, \ldots, \lambda_n\) be the eigenvalues of its adjacency matrix; the Estrada index \(E E \left(G\right)\) of the graph \(G\) is defined as the sum of the terms \(e^{\lambda i}\), \(i = 1,2, \ldots, n\). The \(n\)-dimensional folded hypercube networks \(F Q_n\) are an important and attractive variant of the \(n\)-dimensional hypercube networks \(Q_n\), which are obtained from \(Q_n\) by adding an edge between any pair of vertices complementary edges. In this paper, we establish the explicit formulae for calculating the Estrada index of the folded hypercubes networks \(F Q_n\) by deducing the characteristic polynomial of the adjacency matrix in spectral graph theory. Moreover, some lower and upper bounds for the Estrada index of the folded hypercubes networks \(F Q_n\) are proposed.