Estrada index and Chebyshev polynomials

Abstract

Let G be a graph whose eigenvalues are λ 1, λ 2,…, λ n . The Estrada index of G is equal to ∑ i = 1 n e λ i . We point out certain classes of graphs whose characteristic polynomials are closely connected to the Chebyshev polynomials of the second kind. Various relations, in particular approximations, for the Estrada index of these graphs are obtained.