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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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[1] Ş.B.B. Altındağ, I.Ž. Milovanović, E.I. Milovanović, and M.M. Matejić, Modified hyper-Wiener index of trees, Discrete Appl. Math. 334 (2023), 101–109. https://doi.org/10.1016/j.dam.2023.03.005
[2] X. Chen and J. Qian, Bounding the sum of powers of the Laplacian eigenvalues of graphs, Appl. Math. J. Chin. Univ. 26 (2011), no. 2, 142–150. https://doi.org/10.1007/s11766-011-2732-4
[3] K.C. Das, K. Xu, and M. Liu, On sum of powers of the Laplacian eigenvalues of graphs, Linear Algebra Appl. 439 (2013), no. 11, 3561–3575. https://doi.org/10.1016/j.laa.2013.09.036
[4] A.A. Dobrynin, R. Entringer, and I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math. 66 (2001), no. 3, 211–249. https://doi.org/10.1023/A:1010767517079
[5] S. Fajtlowicz, On conjectures of Graffiti II, Congr. Numer. 60 (1987), 187–197.
[6] R. Grone and R. Merris, The Laplacian spectrum of a graph II, SIAM J. Discrete Math. 7 (1994), no. 2, 221–229. https://doi.org/10.1137/S0895480191222653
[7] J.L. Gross, J. Yellen, and M. Anderson, Graph Theory and Its Applications, CRC Press, New York, 2018.
[8] I. Gutman, Hyper-Wiener index and Laplacian spectrum, J. Serb. Chem. Soc. 68 (2003), no. 12, 949–952.
[9] I. Gutman, B. Furtula, and J. Belić, Note of the hyper-Wiener index, J. Serb. Chem. Soc. 68 (2003), no. 12, 943–948. http://dx.doi.org/10.2298/JSC0312943G [10] I. Gutman, S.L. Lee, C.H. Chu, and Y.L. Luo, Chemical applications of the Laplacian spectrum of molecular graphs: studies of the Wiener number, Indian J. Chem. 33A (1994), no. 7, 603–608.
[11] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total $\phi$–electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538. https://doi.org/10.1016/0009-2614(72)85099-1
[12] J.L.W.V. Jensen, Sur les fonctions convexes et les in´egalit´es entre les valeurs moyennes, Acta math. 30 (1906), no. 1, 175–193. https://doi.org/10.1007/BF02418571
[13] M. Liu and B. Liu, A note on sum of powers of the Laplacian eigenvalues of graphs, Appl. Math. Lett. 24 (2011), no. 3, 249–252. https://doi.org/10.1016/j.aml.2010.09.013
[14] R. Merris, Laplacian matrices of graphs: A survey, Linear Algebra Appl. 197–198 (1994), 143–176. https://doi.org/10.1016/0024-3795(94)90486-3
[15] I.Ž. Milovanović, E.I. Milovanović, M. Matejić, and A. Ali, Some new bounds on the modified first Zagreb index, Commun. Comb. Optim. 8 (2023), no. 1, 13–21. https://doi.org/10.22049/cco.2021.27159.1205
[16] D.S. Mitrinović, J. Pečarić, and A.M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.
[17] D.S. Mitrinović and P.M. Vasić, Analytic Inequalities, Springer Verlag, Berlin–Heidelberg–New York, 1970.
[18] B. Mohar, D. Babić, and N. Trinajstić, A novel definition of the Wiener index for trees, J. Chem. Inf. Comput. 33 (1993), no. 1, 153–154. https://doi.org/10.1021/ci00011a023
[19] S. Nikolić, G. Kovačević, A. Miličević, and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), no. 2, 113–124.
[20] M. Randić, Novel molecular descriptor for structure–property studies, Chem. Phys. Lett. 211 (1993), no. 4-5, 478–483. https://doi.org/10.1016/0009-2614(93)87094-J [21] S. Wagner and H. Wang, Introduction to Chemical Graph Theory, CRC Press, Boca Raton, 2018.
[22] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947), no. 1, 17–20. https://doi.org/10.1021/ja01193a005
[23] B. Zhou, On sum of powers of the Laplacian eigenvalues of graphs, Linear Algebra Appl. 429 (2008), no. 8-9, 2239–2246. | ||
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