Trees with maximum multiplicative connectivity indices
Mahdieh Azarimahdie.azari@gmail.commahdieh.azari@iau.ac.irDepartment of MathematicsKazerun BranchIslamic Azad UniversityKazerun, P. O. Box: 73135-168, Iran0000-0002-0919-0598View full profile → , *Nasrin DehgardiCorresponding authorn.dehgardi@sirjantech.ac.irDepartment of Mathematics and Computer ScienceSirjan University of TechnologySirjan, Iran0000-0001-8214-6000View full profile →
* Corresponding author · click or hover a name for details
- Published Online:
- 30 Nov 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1862
- Pages:
- 1517–1529
Abstract
Keywords
Subject Classifications
References
[1] A. Ali, Counter examples to a conjecture concerning harmonic index, Asian-Eur. J. Math., 11 no. 03, 1850035 (2018).
[2] A. Ali, I. Gutman, E. Milovanović and I. Milovanović, Sum of powers of the degrees of graphs: Extremal results and bounds, MATCH Commun. Math. Comput. Chem., 80, 5-84 (2018).
[3] A. Ali and T. Idrees, A note on polyomino chains with extremum general sum-connectivity index, Commun. Comb. Optim., 6 no. 01, 81-91 (2021).
[4] M. Azari and A. Iranmanesh, Atom-bond connectivity index, in New Frontiers in Nanochemistry: Concepts, Theories and Trends, Vol. II: Topological Nanochemistry, ed. By M. V. Putz, Apple Academics Press & CRC Press at Taylor & Francis, Waretown, NJ, pp. 1-18 (2020).
[5] M. Azari and A. Iranmanesh, Geometric-arithmetic index, in New Frontiers in Nanochemistry: Concepts, Theories and Trends, Vol. II: Topological Nanochemistry, ed. by M. V. Putz, Apple Academics Press & CRC Press at Taylor & Francis, Waretown, NJ, pp. 227-248 (2020).
[6] M. Bhanumathi and K. E. J. Rani, On multiplicative sum connectivity index, multiplicative Randic index and multiplicative harmonic index of some nanostar dendrimers, Int. J. Adv. Sci. Eng. Sci. Adv. Comput. Bio-Technol., 9 no. 2, 52-67 (2018).
[7] A. Bharali and R. Bora, Computation of some degree based topological indices of silicates (SiO2) layer, Ann. Pure Appl. Math., 16 no. 2, 287-293 (2018).
[8] B. Borovicanin, K. C. Das, B. Furtula and I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem., 78, 17-100 (2017).
[9] K. C. Das, S. Das and B. Zhou, Sum-connectivity index of a graph, Front. Math. China, 11, 47-54 (2016).
[10] N. Dehgardi and H. Aram, Sharp bounds on the augmented Zagreb index of graph operations, Kragujevac J. Math., 44 no. 4, 509-522 (2020).
[11] M. V. Diudea, QSPR/QSAR Studies by Molecular Descriptors, Nova Science, Huntingdon, New York, USA (2000).
[12] M. Eliasi, A. Iranmanesh and I. Gutman, Multiplicative versions of first Zagreb index, MATCH Commun. Math. Comput. Chem., 68, 217-230 (2012).
[13] E. Estrada, L. Torres, L. Rodriguez and I. Gutman, An atom-bond connectivity index, Modelling the entalphy of formation of alkanes, Indian J. Chem., 37A no. 10, 849-855 (1998).
[14] S. Fajtlowicz, On conjectures of Graffiti-II, Congr. Numer., 60, 187-197 (1987).
[15] B. Furtula, A. Graovac and D. Vukičević, Augmented Zagreb index, J. Math. Chem., 48 no. 2, 370-380 (2010).
[16] P. Gayathri and S. Sunantha, Multiplicative connectivity indices of TUC4C8(R) nanotube, Int. J. Math. Appl., 6 no. 2-B, 443-455 (2018).
[17] P. Gayathri and S. Sunantha, Multiplicative indices of TUC4C6C8[m, n] nanotube and C4C6C8[m, n] nanotori, Malaya J. Mat., 7 no. 3, 561-565 (2019).
[18] I. Gutman, B. Furtula and V. Katanić, Randić index and information, AKCE Int. J. Graphs Comb., 15 no. 3, 307-312 (2018).
[19] I. Gutman, E. Milovanović and E. Milovanović, Beyond the Zagreb indices, AKCE Int. J. Graphs Comb., 17 no. 1, 74-85 (2020).
[20] I. Gutman, B. Rušcić, N. Trinajstić and C. F. Wilcox, Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys., 62, 3399-3405 (1975).
[21] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, 535-538 (1972).
[22] V. R. Kulli, Multiplicative connectivity indices of certain nanotubes, Ann. Pure Appl. Math., 12 no. 2, 169-176 (2016).
[23] V. R. Kulli, Multiplicative connectivity indices of TUC4C8[m, n] and TUC4 [m, n] nanotubes, J. Comput. Math. Sci., 7 no. 11, 599-605 (2016).
[24] V. R. Kulli, Computation of multiplicative connectivity indices of H-naphtalenic nanotubes and TUC4 [m, n] nanotubes, J. Comput. Math. Sci., 9 no. 8, 1047-1056 (2018).
[25] X. Li and Y. Shi, A survey on the Randić index, MATCH Commun. Math. Comput. Chem., 59, 127-156 (2008).
[26] M. Liang, B. Cheng and J. Liu, Solution to the minimum harmonic index of graphs with given minimum degree, Trans. Comb., 7 no. 2, 25-33 (2018).
[27] B. Lučić, N. Trinajstić and B. Zhou, Comparison between the sum-connectivity index and product-connectivity index for benzenoid hydrocarbons, Chem. Phys. Lett., 475, 146-148 (2009).
[28] K. G. Mirajkar and B. Pooja, Some multiplicative topological indices of silicates networks, J. Emerg. Technol. Innov., 6 no. 3, 380-390 (2019).
[29] S. Mondal, N. De and A. Pal, Multiplicative degree based topological indices of nanostar dendrimers, Biointerface Res. Appl. Chem., 11 no. 1, 7700-7711 (2021).
[30] M. Randić, On characterization of molecular branching, J. Amer. Chem. Soc., 97, 6609-6615 (1975).
[31] M. Randić, The connectivity index 25 years after, J. Mol. Graph. Model., 20, 19-35 (2001).
[32] J. M. Rodríguez and J. M. Sigarreta, New results on the harmonic index and its generalizations, MATCH Commun. Math. Comput. Chem., 78, 387-404 (2017).
[33] P. Sarkar, N. De and A. Pal, On some multiplicative version topological indices of block shift and hierarchical hypercube networks, OPSEARCH, 59, 561-572 (2022).
[34] Z. Shao, A. Jahanbani and S. M. Sheikholeslami, Multiplicative topological indices of molecular structure in anticancer drugs, Polycycl. Aromat. Compd., 42 no. 2, 475-488 (2022).
[35] B. Shwetha Shetty, V. Lokesha and P. S. Ranjini, On the harmonic index of graph operations, Trans. Comb., 4 no. 4, 5-14 (2015).
[36] R. Todeschini and V. Consonni, New local vertex invariants and descriptors based on functions of vertex degrees, MATCH Commun. Math. Comput. Chem., 64, 359-372 (2010).
[37] N. Trinajstić, Chemical Graph Theory, CRC Press, Boca Raton, FL (1992).
[38] T. Vetrík, General sum-connectivity index of trees with given number of branching vertices, Trans. Comb., 12 no. 4, 227-238 (2023).
[39] D. Vukičević and B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem., 46, 1369-1376 (2009).
[40] S. Wang, B. Zhou and N. Trinajstić, On the sum-connectivity index, Filomat, 25 no. 3, 29-42 (2011).
[41] R. Xing, B. Zhou and N. Trinajstić, Sum-connectivity index of molecular trees, J. Math. Chem., 48, 583-591 (2010).
[42] B. Zhou and N. Trinajstić, On a novel connectivity index, J. Math. Chem., 46, 1252-1270 (2009).
