ON THE SPECTRA OF TERMINAL DISTANCE MATRIX OF GRAPHS

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 spectra of the reduced distance matrix of the generalized Bethe trees. As application, we compute the spectrum of the reduced distance matrix of regular dendrimers. Finally, the spectrum of thorn graphs will be computed.