on the spectra of reduced distance matrix of the generalized bethe trees

Let g be a simple connected graph and {v_1,v_2,..., v_k} be the set of pendent (vertices of degree one) vertices of g. the reduced distance matrix of g is a square matrix whose (i,j)-entry is the topological distance between v_i and v_j of g. in this paper, we compute the spectrum of the reduced distance matrix of the generalized bethe trees.