Some Properties on Estrada Index of Folded Hypercubes Networks

Let G be a simple graph with n vertices and let λ1, λ2, …, λn be the eigenvalues of its adjacency matrix; the Estrada index EE(G) of the graph G is defined as the sum of the terms eλi, i = 1,2, …, n. The n‐dimensional folded hypercube networks FQn are an important and attractive variant of the n‐dimensional hypercube networks Qn, which are obtained from Qn 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 FQn 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 FQn are proposed.