Some Bounds for Summation of the Second and the Third Power of D-Eigenvalues

The D- eigenvalues {Λ1,Λ2,...,Λn} of a graph G are the eigenvalues of its distance matrix D. The distance matrix D = D(G) of G is defined so that its (i,j) entry is equal to d(vi,vj) , the distance between the vertices vi and vj of G. In this paper we find some bounds for summation of the second and third power of D-eigenvalues.