Some Properties on Estrada Index of Folded Hypercubes Networks

Let be a simple graph with vertices and let be the eigenvalues of its adjacency matrix; the Estrada index of the graph is defined as the sum of the terms , . The -dimensional folded hypercube networks are an important and attractive variant of the -dimensional hypercube networks , which are obtained from 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 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 are proposed.