On the Spectra of Reduced Distance Matrix of the Generalized Bethe Trees

Let G be a simple connected graph and {V1, V2, V3, ..., Vk} be the set of pendant (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix of order k whose (i, j)-entry is the topological distance between V; and v; of G. A rooted tree is called a neralized Bethe tree if its vertices at the same level have equal degree. In this paper, we compute the spectrum of the reduced distance matrix of the generalized Bethe trees.