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On relations between the modified hyper Wiener index and some degree based indices of trees | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 21، دوره 11، شماره 2، شهریور 2026، صفحه 685-694 اصل مقاله (372.67 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29529.2040 | ||
| نویسندگان | ||
| Ş.B. Bozkurt Altındağ* 1؛ I. Milovanovic2؛ E. Milovanovic2 | ||
| 1Department of Mathematics, Faculty of Science, Selçuk University, Konya, Turkey | ||
| 2Faculty of Electronic Engineering, University of Niš, Niš, Serbia | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| graph؛ Laplacian eigenvalues؛ modified hyper-Wiener index | ||
| مراجع | ||
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