EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 59 / No 4 (July-August 2025) RAIRO-Oper. Res., 59 4 (2025) 2201-2212 References
Open Access
Issue
RAIRO-Oper. Res.
Volume 59, Number 4, July-August 2025
Page(s) 2201 - 2212
DOI https://doi.org/10.1051/ro/2025086
Published online 14 August 2025
  • F. Harary, Graph Theory. Addison-Wesley, Reading (1972). [Google Scholar]
  • E.R. Scheinerman and D.H. Ullman, Fractional Graph Theory: A Rational Approach to the Theory of Graphs. Dover Publications, United States (2013). [Google Scholar]
  • J.C. Dearden, The use of topological indices in QSAR and QSPR modeling, in Advances in QSAR Modeling, edited by K. Roy Springer, Cham (2017) 57–88. [Google Scholar]
  • I. Gutman, Degree-based topological indices. Croatica Chemica Acta 86 (2013) 351–361. [Google Scholar]
  • I. Gutman and N. Trinajstić, Graph theory and molecular orbitals: total ø-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17 (1972) 535–538. [Google Scholar]
  • I. Gutman, B. Ruščić, N. Trinajstić and C.F. Wilcox, Graph theory and molecular orbitals. XII. Acyclic Polyenes. J. Chem. Phys. 62 (1975) 3399–3405. [Google Scholar]
  • B. Furtula and I. Gutman, A forgotten topological index. J. Math. Chem. 53 (2015) 1184–1190. [Google Scholar]
  • M. Liu and B. Liu, The second Zagreb indices and Wiener polarity indices of trees with given degree sequences. MATCH Commun. Math. Comput. Chem. 67 (2012) 439. [Google Scholar]
  • B. Borovićanin, B. Furtula and I. Gutman, Bounds for Zagreb indices. MATCH Commun. Math. Comput. Chem. 78 (2017) 17–100. [Google Scholar]
  • H. Abdo, D. Dimitrov and I. Gutman, On the Zagreb indices equality. Discrete Appl. Math. 160 (2012) 1–8. [Google Scholar]
  • M. Javaid, S. Javed, S.Q. Memon and A.M. Alanazi, Forgotten index of generalized operations on graphs. J. Chem. 2021 (2021) 1–14. [Google Scholar]
  • I.Z. Milovanović, E. Milovanović, I. Gutman and B. Furtula, Some inequalities for the forgotten topological index. Int. J. Appl. Graph Theory 1 (2017) 1–15. [Google Scholar]
  • I. Gutman, Geometric approach to degree-based topological indices: Sombor indices. MATCH Commun. Math. Comput. Chem. 86 (2021) 11–16. [Google Scholar]
  • H. Liu, I. Gutman, L. You and Y. Huang, Sombor index: review of extremal results and bounds. J. Math. Chem. 60 (2022) 771–798. [Google Scholar]
  • F. Movahedi and M.H. Akhbari, Degree-based topological indices of the molecular structure of hyaluronic acid-methotrexate conjugates in cancer treatment. Int. J. Quantum. Chem. 123 (2023) e27106. [Google Scholar]
  • T. Zhou, Z. Lin and L. Miao, The Sombor index of trees and unicyclic graphs with given maximum degree. Discrete Math. Lett. 7 (2021) 24–29. [Google Scholar]
  • F. Movahedi and M.H. Akhbari, Entire Sombor index of graphs. Iran. J. Math. Chem. 14 (2023) 33–45. [Google Scholar]
  • H. Liu, H. Chen, Q. Xiao, X. Fang and Z. Tang, More on Sombor indices of chemical graphs and their applications to the boiling point of benzenoid hydrocarbons. Int. J. Quantum Chem. 121 (2021) e26689. [Google Scholar]
  • I. Gutman, B. Furtula and M.S. Oz, Geometric approach to vertex-degree-based topological indices-Elliptic Sombor index, theory and application. Int. J. Quantum Chem. 124 (2024) e27346. [Google Scholar]
  • C. Espinal, I. Gutman and J. Rada, Elliptic Sombor index of chemical graphs. Commun. Comb. Optim. 10 (2025) 989–999. [Google Scholar]
  • J. Rada, J.M. Rodríguez and J.M. Sigarreta, Sombor index and elliptic Sombor index of benzenoid systems. Appl. Math. Comput. 475 (2024) 128756. [Google Scholar]
  • V.R. Kulli, Modified elliptic Sombor index and its exponential of a graph. Int. J. Math. Comput. Res. 12 (2024) 3949–3954. [Google Scholar]
  • F. Qi and Z. Lin, Maximal elliptic Sombor index of bicyclic graphs. Contrib. Math. 10 (2024) 5–29. [Google Scholar]
  • N. Ghanbari and S. Alikhani, Elliptic Sombor index of graphs from primary subgraphs. Anal. Numer. Solut. Non-linear Equ. 8 (2023) 127–140. [Google Scholar]
  • J. Rada, J.M. Rodríguez and J.M. Sigarreta, Optimization problems for general elliptic Sombor index. MATCH Commun. Math. Comput. Chem. 93 (2025) 819–838. [Google Scholar]
  • B. Kirana, M.C. Shanmukha and A. Usha, Comparative study of Sombor index and its various versions using regression models for top priority polycyclic aromatic hydrocarbons. Sci. Rep. 14 (2024) 19841. [Google Scholar]
  • F. Movahedi, Relations between elliptic Sombor index and some known topological indices. Asian-Eur. J. Math. Accepted June 3, 2025. DOI: 10.1142/S1793557125500603. [Google Scholar]
  • M. Biernacki, H. Pidek and C. Ryll-Nardzewski, Sur une iněgalitě entre des intěgrales děfinies. Ann. Univ. Mariae Curie-Skolodowska A4 (1950) 1–4. [Google Scholar]
  • J.B. Diaz and F.T. Metcalf, Stronger forms of a class of inequalities of G, Pólya-G. Szeg o, and L.V, Kantorovich. Bull. Amer. Math. Soc. 69 (1963) 415–419. [Google Scholar]
  • G.H. Hardy, J.E. Littlewood and G. Polya, Inequalities. Cambridge University Press (1952). [Google Scholar]
  • K.C. Das, Sharp bounds for the sum of the squares of the degrees of a graph. Kragujevac J. Math. 25 (2003) 31–49. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.