On relations between the modified hyper Wiener index and some degree based indices of trees

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, Faculty of Science, Selçuk University, Konya, Turkey

2 Faculty of Electronic Engineering, University of Niš, Niš, Serbia

Abstract

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.

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References

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Communications in Combinatorics and Optimization

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Available Online from 01 September 2024

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