on relations between the modified hyper wiener index and some degree based indices of trees

Let t be a tree of order n with laplacian eigenvalues $mu_{1}geq mu_{2}geq cdots geq mu_{n-1}>mu_{n}=0$. the wiener index of t is defined as $w(t)=nsum_{i=1}^{n-1} frac{1}{mu_i }$. the modified hyper wiener index of t is stated in terms of w(t) and laplacian eigenvalues as $www(t)= frac{w(t)^2}{2n}-frac{n}{2}sum_{i=1}^{n-1} frac{1}{mu_i^2}$. in this study, we present some relations between modified hyper-wiener index, the first zagreb index, modified first zagreb index and inverse degree index of trees when order n and maximal vertex degree of a graph are known.