Abstract

The Bethe trees are unweighted rooted trees of k levels whose root vertex has degree d, the vertices from 2 to level k -1 have degree d + 1 and the vertices at level k have degree 1. This paper gives an explicit formula for the energy and an approximation to the Estrada index of Bethe trees. We also obtain an explicit formula for the energy and an approximation for the Estrada index of double Bethe trees, that are unions of two Bethe trees with common root vertex.