On Relations between Atom-Bond Sum-Connectivity Index and other Degree-Based Indices

Document Type : Research Paper

Authors

Department of Mathematics‎, ‎Manipal Institute of Technology Manipal Academy of Higher Education, ‎Manipal‎, ‎India‎ -- ‎576104

Abstract

‎The atom-bond sum-connectivity $(ABS)$ index is a novel vertex degree-based topological index defined recently as‎,
‎$ABS(G)=\sum\limits_{i\simj}\sqrt{\frac{d_{i}+d_{j}-2}{d_{i}+d_{j}}}=\sum\limits_{i\sim j}\sqrt{1-\frac{2}{d_{i}+d_{j}}},$ where $d_{i},d_{j}$ are degrees of vertices $i$ and $j$ respectively‎. ‎New findings linking the $ABS$-index to extensively researched topological indices are presented in this work.

Keywords

Main Subjects

References

[1] K. C. Das, J. M. Rodríguez García and J. M. Sigarreta, On the generalized abc index of graphs, MATCH Commun. Math. Comput. Chem. 87 (2022) 147–169, https://doi.org/10.46793/match.87-1.147D.
[2] M. Randic, Characterization of molecular branching, J. Am. Chem. Soc. 97 (1975) 6609–6615, https://doi.org/10.1021/ja00856a001.
[3] B. Zhou and N. Trinajstic, On a novel connectivity index, J. Math. Chem. 46 (2009) 1252–1270, https://doi.org/10.1007/s10910-008-9515-z.
[4] B. Zhou and N. Trinajstic, On general sum-connectivity index, J. Math. Chem. 47 (2010) 210–218, https://doi.org/10.1007/s10910-009-9542-4.
[5] S. Fajtlowicz, On conjectures of graffiti, Ann. Discrete Math. 38 (1988) 113–118, https://doi.org/10.1016/S0167-5060(08)70776-3.
[6] I. Gutman and N. Trinajstic, Graph theory and molecular orbitals, total $\phi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538, https://doi.org/10.1016/0009-2614(72)85099-1.
[7] G. H. Shirdel, H. Rezapour and A. M. Sayadi, The hyper-zagreb index of graph operations, Iranian J. Math. Chem. 4 (2013) 213–220, https://doi.org/10.22052/IJMC.2013.5294.
[8] B. Furtula, A. Graovac and D. Vukicevic, Augmented zagreb index, J. Math. Chem. 48 (2010) 370–380, https://doi.org/10.1007/s10910-010-9677-3.
[9] V. Kulli, F-indices of chemical networks, Int. J. Math. Archive 10 (2019) 21–30.
[10] E. Estrada, L. Torres, L. Rodriguez and I. Gutman, An atom-bond connectivity index: modelling the enthalpy of formation of alkanes, Indian J. Chem. 37A (1998) 849–855.
[11] A. Ali, D. Dimitrov, Z. Du and F. Ishfaq, On the extremal graphs for general sumconnectivity index ($\chi_\alpha$) with given cyclomatic number when   = 1, Discrete Appl. Math. 257 (2019) 19–30, https://doi.org/10.1016/j.dam.2018.10.009.
[12] A. Ali, B. Furtula, I.Redžepovic and I. Gutman, Atom-bond sum-connectivity index, J. Math. Chem. 60 (2022) 2081–2093, https://doi.org/10.1007/s10910-022-01403-1.
[13] A. Ali, I. Gutman and I. Redžepovic, Atom-bond sum-connectivity index of unicyclic graphs and some applications, Electron. J. Math. 5 (2023) 1–7, https://doi.org/10.47443/ejm.2022.039.
[14] T. A. Alraqad, I. Z. Milovanovic, H. Saber, A. Ali, J. P. Mazorodze and A. A. Attiya, Minimum atom bond sum-connectivity index of trees with a fixed order and/or number of pendent vertices, AIMS Math. 9 (2024) 3707–3721, https://doi.org/10.3934/math.2024182.
[15] P. Nithya, S. Elumalai, S. Balachandran and S. Mondal, Smallest abs index of unicyclic graphs with given girth, J. Appl. Math. Comput. 69 (2023) 3675–3692, https://doi.org/10.1007/s12190-023-01898-0.
[16] S. Noureen and A. Ali, Maximum atom-bond sum-connectivity index of border trees with fixed number of leaves, Discrete Math. Lett. 12 (2023) 26–28, https://doi.org/10.47443/dml.2023.016.
[17] X. Zuo, A. Jahanbani and H. Shooshtari, On the atom-bond sumconnectivity index of chemical graphs, J. Mol. Struct. 1296 (2024) #136849, https://doi.org/10.1016/j.molstruc.2023.136849.
[18] T. Alraqad, H. Saber, A. Ali and A. M. Albalahi, On the maximum atom-bond sumconnectivity index of graphs, Open Math. 22 (2014) #20230179.
[19] A. Ali, I. Milovanovic, E. Milovanovic and M. Matejic, Sharp inequalities for the atom–bond (sum) connectivity index, J. Math. Inequal. 17 (2023) 1411–1426, https://doi.org/10.7153/jmi-2023-17-92.
[20] Z. Lin, On relations between atom-bond sum-connectivity index and other connectivity indices, Bull. Int. Math. Virtual Inst. 13 (2023) 249–252.
[21] Y. Ge, Z. Lin and J. Wang, Atom-bond sum-connectivity index of line graphs, Discrete Math. Lett. 12 (2023) 196–200, https://doi.org/10.47443/dml.2023.197.
[22] A. M. Albalahi, Z. Du and A. Ali, On the general atom-bond sum-connectivity index, AIMS Math. 8 (2023) 23771–23785, https://doi.org/10.3934/math.20231210.
[23] A. M. Albalahi, E. Milovanovic and A. Ali, General atom-bond sum-connectivity index of graphs, Mathematics 11 (2023) #2494, https://doi.org/10.3390/math11112494.
[24] A. Jahanbani and I.Redžepovic, On the generalized abs index of graphs, Filomat 37 (2023) 10161–10169, https://doi.org/10.2298/FIL2330161J.
[25] S. Filipovski, Relations between sombor index and some degreebased topological indices, Iranian J. Math. Chem. 12 (2021) 19–26, https://doi.org/10.22052/IJMC.2021.240385.1533.
[26] Z. Wang, Y. Mao, Y. Li and B. Furtula, On relations between sombor and other degreebased indices, J. Appl. Math. Comput. 68 (2022) 1–17, https://doi.org/10.1007/s12190-021-01516-x.
[27] K. Xu, K. C. Das and N. Trinajstic, Relation between the harary index and related topological indices, The Harary Index of a Graph (2015) 27–34.
[28] D. S. Mitrinovic and P. M. Vasic, Analytic Inequalities, Berlin: Springer 1970.
[29] N. Ozeki, On the estimation of the inequalities by the maximum, or minimum values, J. College Arts Sci. Chiba Univ. 5 (1969) 199–203.
[30] J. Radon, Theorie und Anwendungen der absolut additiven Mengenfunktionen, Holder, 1913.
[31] Z. Latreuch and B. Belaıdi, New inequalities for convex sequences with applications, Int. J. Open Problems Comput. Math. 5 (2012) 15–27.
[32] S. S. Dragomir, A survey on cauchy-bunyakovsky-schwarz type discrete inequalities, JIPAM. J. Inequal. Pure Appl. Math. 4 (2003) 1–142.
[33] Z. Hussain, H. Liu, S. Zhang and H. Hua, Bounds for the atom-bond sum-connectivity index of graphs, Research Square (2023) https://doi.org/10.21203/rs.3.rs-3353933/v1.
[34] A. Martínez-Pérez, J. M. Rodríguez and J. M. Sigarreta, CMMSE: a new approximation to the geometric–arithmetic index, J. Math. Chem. 56 (2018) 1865–1883, https://doi.org/10.1007/s10910-017-0811-3.
[35] ] S. M. Hosamani and B. Basavanagoud, New upper bounds for the first zagreb index, MATCH Commun. Math. Comput. Chem 74 (2015) 97–101.
[36] K. J. Gowtham and I. Gutman, On the difference between atom-bond sum-connectivity and sum-connectivity indices, Bulletin (Académie serbe des sciences et des arts. Classe des sciences mathématiques et naturelles. Sciences mathématiques) 47 (2022) 55–66.
[37] Z. Du, A. Jahanbai and S. M. Sheikholeslami, Relationships between randic index and other topological indices, Commun. Comb. Optim. 6 (2021) 137–154.
[38] Y. Huang, B. Liu and L. Gan, Augmented zagreb index of connected graphs, MATCH Commun. Math. Comput. Chem. 67 (2012) 483–494.
Iranian Journal of Mathematical Chemistry
Volume 15, Issue 4
December 2024
Pages 283-295

Files

Share

How to cite

Statistics