آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 123 |
| تعداد مقالات | 1,561 |
| تعداد مشاهده مقاله | 1,672,675 |
| تعداد دریافت فایل اصل مقاله | 1,559,828 |
Some new bounds on the modified first Zagreb index | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 8، شماره 1، خرداد 2023، صفحه 13-21 اصل مقاله (354.66 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.27159.1205 | ||
| نویسندگان | ||
| Igor Milovanović1؛ Emina Milovanović2؛ Marjan Matejić2؛ Akbar Ali* 3 | ||
| 1Faculty of Electronic Engineering, University of Nis, Nis, Serbia | ||
| 2Faculty of Electronic Engineering | ||
| 3University of Hail, Saudi Arabia | ||
| چکیده | ||
| Let $G$ be a graph containing no isolated vertices. For the graph $G$, its modified first Zagreb index is defined as the sum of reciprocals of squares of vertex degrees of $G$. This article provides some new bounds on the modified first Zagreb index of $G$ in terms of some other well-known graph invariants of $G$. From the obtained bounds, several known results follow directly. | ||
| کلیدواژهها | ||
| degree-based topological index؛ modified first Zagreb index؛ inverse degree | ||
| مراجع | ||
|
[1] A. Ali, I. Gutman, E.I. Milovanović, and I.Z. Milovanović, Sum of powers of the degrees of graphs: extremal results and bounds, MATCH Commun. Math. Comput. Chem. 80 (2018), no. 1, 5–84.
[2] K.C. Das, K. Xu, and J. Wang, On inverse degree and topological indices of graphs, Filomat 30 (2016), no. 8, 2111–2120.
[3] S. Fajtlowicz, On conjectures of Graffiti-II, Congr. Numer. 60 (1987), 187–197.
[4] I. Gutman, Degree–based topological indices, Croat. Chem. Acta 86 (2013), no. 4, 351–361.
[5] I. Gutman, K.C. Das, B. Furtula, E.I. Milovanović, and I.Z. Milovanović, Generalizations of Szõkefalvi-Nagy and Chebyshev inequalities with applications in spectral graph theory, Appl. Math. Comput. 313 (2017), 235–244.
[6] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total ϕelectron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538.
[7] J. Hao, Theorems about Zagreb indices and modified Zagreb indices, MATCH Commun. Math. Comput. Chem. 65 (2011), no. 3, 659–670.
[8] J.L.W. Jensen, Sur les fonctions convexes et les in´egalit´es entre les valeurs moyennes, Acta Math. 30 (1906), no. 1, 175–193.
[9] X. Li and H. Zhao, Trees with the first three smallest and largest generalized topological indices, MATCH Commun. Math. Comput. Chem. 50 (2004), 57–62.
[10] C. Liu, J. Li, and Y. Pan, On extremal modified Zagreb indices of trees, MATCH Commun. Math. Comput. Chem. 85 (2021), no. 2, 349–366.
[11] A. Miličević and S. Nikolić, On variable Zagreb indices, Croat. Chem. Acta 77 (2004), no. 1-2, 97–101.
[12] P. Milošević, I.Z. Milovanović, E.I. Milovanović, and M. Matejić, Some inequalities for general zeroth-order Randić index, Filomat 33 (2019), no. 16, 5249–5258.
[13] I.Z. Milovanović, M. Matejić, and E.I. Milovanović, ˇ A note on the general zeroth–order Randi´c coindex of graphs, Contrib. Math. 1 (2020), no. 1, 17–21.
[14] B. Mitić, E.I. Milovanović, M. Matejić, and I.Z. Milovanović, Some properties of the inverse degree index and coindex of trees, Filomat (in press).
[15] D.S. Mitrinović, J.E. Pečarić, and A.M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht–Boston–London, 1993.
[16] D.S. Mitrinović and P. M. Vasić, Analytic Inequalities, Springer Verlag, BerlinHeidelberg-New York, 1970.
[17] S. Nikolić, G. Kovačević, A. Miličević, and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), no. 2, 113–124.
[18] R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley VCH, Weinheim, 2000.
[19] R. Todeschini and V. Consonni, New local vertex invariants and molecular descriptors based on functions of the vertex degrees, MATCH Commun. Math. Comput. Chem. 64 (2010), no. 2, 359–372. | ||
|
آمار تعداد مشاهده مقاله: 974 تعداد دریافت فایل اصل مقاله: 1,718 |
||