Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 2 2026 06 01 On relations between the modified hyper Wiener index and some degree based indices of trees 685 694 14838 10.22049/cco.2024.29529.2040 EN Ş.B. Bozkurt Altındağ Department of Mathematics, Faculty of Science, Selçuk University, Konya, Turkey I. Milovanovic Faculty of Electronic Engineering, University of Niš, Niš, Serbia E. Milovanovic Faculty of Electronic Engineering, University of Niš, Niš, Serbia Journal Article 2024 03 12 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 $W(T)=n\sum_{i=1}^{n-1} \frac{1}{\mu_i }$. 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. https://comb-opt.azaruniv.ac.ir/article_14838_62c761bfb31895fee10a5053d75d97d9.pdf