Bounds of Sombor Index for Corona Products on $R$-Graphs

[1] S. Akhter, R. Farooq, and S. Pirzada, Exact formulae of general sum-connectivity index for some graph operations, Mat. Vesnik 70 (2018), no. 3, 267–282.

[2] S. Akhter, M. Imran, and Z. Raza, Bounds for the general sum-connectivity index of composite graphs, J. Inequal. Appl.  2017 (2017), no. 1, Article number: 76.  https://doi.org/10.1186/s13660–017–1350–y

[3] B. Chaluvaraju and N. Manjunath, PBIB-designs and association schemes arising from minimum bi-connected dominating sets of some special classes of graphs, Afr. Mat. 29 (2018), no. 1, 47–63.  https://doi.org/10.1007/s13370–017–0525–5

[4] K.C. Das, A.S. Çevik, I.N. Cangul, and Y. Shang, On Sombor index, Symmetry 13 (2021), no. 1, Article number: 140.  https://doi.org/10.3390/sym13010140

[5] K.C. Das, A. Yurttas, M. Togan, A.S. Çevik, and I.N. Cangul, The multiplicative Zagreb indices of graph operations, J. Inequal. Appl. 2013 (2013), no. 1, Article number 90.  https://doi.org/10.1186/1029–242X–2013–90

[6] T. Došlic, T. Réti, and A. Ali, On the structure of graphs with integer Sombor indices, Discrete Math. Lett 7 (2021), 1–4. https://doi.org/10.47443/dml.2021.0012

[7] G.H. Fath-Tabar, B. Vaez-Zadeh, A.R. Ashrafi, and A. Graovac, Some inequalities for the atom-bond connectivity index of graph operations, Discrete Appl. Math. 159 (2011), no. 13, 1323–1330.  https://doi.org/10.1016/j.dam.2011.04.019

[8] W. Gao, Z. Iqbal, M. Ishaq, A. Aslam, M. Aamir, and M.A. Binyamin, Bounds on topological descriptors of the corona product of F-sum of connected graphs, IEEE Access 7 (2019), 26788–26796.  https://doi.org/10.1109/ACCESS.2019.2900061

[9] I. Gutman, Degree-based topological indices, Croatica Chem. Acta 86 (2013), no. 4, 351–361. http://dx.doi.org/10.5562/cca2294

[10] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 1, 11–16.

[11] I. Gutman, Some basic properties of Sombor indices, Open J. Discrete Appl. Math. 4 (2021), no. 1, 1–3.

[12] I. Gutman, E. Milovanović, and I. Milovanović, Beyond the Zagreb indices, AKCE Int. J. G. Comb. 17 (2020), no. 1, 74–85.  https://doi.org/10.1016/j.akcej.2018.05.002

[13] I. Gutman, A.M. Naji, and N.D. Soner, On leap Zagreb indices of graphs, Commun. Comb. Optim. 2 (2017), no. 2, 99–117.  https://doi.org/10.22049/cco.2017.25949.1059

[14] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total ϕ-electron energy of alternant hydrocarbons, Chemical Physics Letters 17 (1972), no. 4, 535–538. https://doi.org/10.1016/0009–2614(72)85099–1

[15] J. Lan and B. Zhou, Spectra of graph operations based on R-graph, Linear Multilinear Algebra 63 (2015), no. 7, 1401–1422. https://doi.org/10.1080/03081087.2014.941292

[16] X. Li and J. Zheng, A unified approach to the extremal trees for different indices, MATCH Commun. Math. Comput. Chem. 54 (2005), no. 1, 195–208.

[17] H. Liu, I. Gutman, L. You, and Y. Huang, Sombor index: Review of extremal results and bounds, J. Math. Chem. 60 (2022), 771–798.  https://doi.org/10.1007/s10910–022–01333–y

[18] M. Liu and B. Liu, Some properties of the first general Zagreb index., Australas. J. Comb. 47 (2010), 285.

[19] D. Maji and G. Ghorai, The first entire Zagreb index of various corona products and their bounds, J. Math. Comput. Sci. 11 (2021), no. 5, 6018–6044.

[20] M. Manjunath, V. Lokesha, Suvarna, and S. Jain, Bounds for the Topological indices of ℘ graph, Eur. J. Pure Appl. Math. 14 (2021), no. 2, 340–350.

[21] I. Milovanović, M. Matejić, E. Milovanović, and R. Khoeilar, A note on the first Zagreb index and coindex of graphs, Commun. Comb. Optim. 6 (2021), no. 1, 41–51.  https://doi.org/10.22049/cco.2020.26809.1144

[22] I. Milovanović, E. Milovanović, and M. Matejić, On some mathematical properties of Sombor indices, Bull. Int. Math. Virtual Inst. 11 (2021), no. 2, 341–353.  https://doi.org/10.7251/BIMVI2102341M

[23] M.R. Oboudi, On graphs with integer Sombor index, J. Appl. Math. Comput. 69 (2023), 941–952.  https://doi.org/10.1007/s12190–022–01778–z

[24] H.S. Ramane, I. Gutman, K. Bhajantri, and D.V. Kitturmath, Sombor index of some graph transformations, Commun. Comb. Optim. 8 (2023), no. 1, 193–205.  https://doi.org/10.22049/cco.2021.27484.1272

[25] M. Randić, On characterization of molecular branching, J. Am. Chem. Soc. 97 (1975), 6609–6615.  https://doi.org/10.1021/ja00856a001

[26] P.S.W. Ranjini and V. Lokesha, SK indices of graph operator S(G) and R(G) on few nanostructures, Montes Taurus J. Pure Appl. Math. 2 (2020), no. 2, 38–44.

[27] P.G. Sheeja, P.S. Ranjini, V. Lokesha, and A.S. Çevik, Computation of the SK index over different corona products of graphs, Palestine J. Math. 10 (2021), no. 1, 8–16.

[28] B. Zhou and N. Trinajstić, On a novel connectivity index, J. Math. Chem. 46 (2009), no. 4, 1252–1270. https://doi.org/10.1007/s10910–008–9515–z

[29] B. Zhou and N. Trinajstić, On general sum-connectivity index, J. Math. Chem. 47 (2010), no. 1, 210–218.  https://doi.org/10.1007/s10910–009–9542–4

[30] 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.  https://doi.org/10.47443/dml.2021.0035