Geometric-arithmetic index-energy predicting the physical properties of alkanes

[1] A. Ali, A.A. Bhatti, and Z. Raza, Further inequalities between vertex-degree-based topological indices, Int. J. Appl. Comput. Math. 3 (2017), no. 3, 1921–1930.  https://doi.org/10.1007/s40819-016-0213-4

[2] M. Aouchiche, I. El Hallaoui, and P. Hansen, Geometric-arithmetic index and minimum degree of connected graphs, MATCH Commun. Math. Comput. Chem. 83 (2020), no. 1, 179–188.

[3] M. Aouchiche and V. Ganesan, Adjusting geometric-arithmetic index to estimate boiling point, MATCH Commun.  Math. Comput. Chem. 84 (2020), no. 2, 483–497.

[4] M. Aouchiche and P. Hansen, The normalized revised Szeged index, MATCH Commun. Math. Comput. Chem. 67 (2012), no. 2, 369–381.

[5] M. Aouchiche and P. Hansen, Comparing the geometric-arithmetic index and the spectral radius of graphs, MATCH Commun. Math. Comput. Chem. 84 (2020), no. 2, 473–482.

[6] A.E. Brouwer and W.H. Haemers, Spectra of Graphs, Springer Science & Business Media, 2010.

[7] G. Caporossi, Variable neighborhood search for extremal vertices: The AutoGraphiX-III system, Comput. Oper. Res. 78 (2017), 431–438.  https://doi.org/10.1016/j.cor.2015.12.009

[8] K.C. Das, I. Gutman, and B. Furtula, Survey on geometric-arithmetic indices of graphs, MATCH Commun. Math. Comput. Chem. 65 (2011), no. 3, 595–644.

[9] T. Divnić, M. Milivojević, and L. Pavlović, Extremal graphs for the geometric–arithmetic index with given minimum degree, Discrete Appl. Math. 162 (2014), 386–390. https://doi.org/10.1016/j.dam.2013.08.001

[10] I. Gutman, The energy of a graph, Ber. Math.–Statist. Sekt. Forsch–ungsz. 103 (1978), 1–22. 

[11] I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes N.Y. 27 (1994), no. 9, 9–15.

[12] I. Gutman and B. Furtula, Geometric-arithmetic indices, Novel Molecular Structure Descriptors—Theory and Applications (I. Gutman and B. Furtula, eds.), Univ. Kragujevac, Kragujevac, 2010, pp. 137–172.

[13] I. Gutman and B. Furtula, Survey of graph energies, Math. Interdisc. Res. 2 (2017), no. 2, 85–129. https://doi.org/10.22052/mir.2017.81507.1057

[14] I. Gutman and B. Furula, Recent Results in the Theory of Randić Index, Univ. Kragujevac, Kragujevac, 2008.

[15]  I. Gutman and B. Furula, Novel Molecular Structure Descriptors - Theory and Applications I, Univ. Kragujevac, Kragujevac, 2010.

[16]  I. Gutman and B. Furula, Novel Molecular Structure Descriptors - Theory and Applications II, Univ. Kragujevac, Kragujevac, 2010.

[17] Y. Hong and X.D. Zhang, Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees, Discrete Math. 296 (2005), no. 2-3, 187–197.  https://doi.org/10.1016/j.disc.2005.04.001

[18] S.M. Hosamani, B.B. Kulkarni, R.G. Boli, and V.M. Gadag, QSPR analysis of certain graph theocratical matrices and their corresponding energy, Appl. Math. Nonlinear Sci. 2 (2017), no. 1, 131–150. https://doi.org/10.21042/AMNS.2017.1.00011

[19] H. Hosoya, Topological index. a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn. 44 (1971), no. 9, 2332–2339.

[20] L.B. Keir and L.H. Hall, Molecular Connectivity in Structural-Activity Analysis, Research study, Letchworth, England, 1986.

[21] L.B. Kier and L.H. Hall, Molecular Connectivity in Chemistry and Drug Research, 1976.

[22] X. Li, I. Gutman, and M. Randić, Mathematical Aspects of Randić-type Molecular Structure Descriptors, University, Faculty of Science, 2006.

[23] X. Li and Y. Shi, A survey on the Randić index, MATCH Commun. Math. Comput. Chem. 59 (2008), no. 1, 127–156.

[24] X. Li, Y. Shi, and I. Gutman, Graph Energy, Springer Science & Business Media, 2012.

[25] V. Nikiforov, Beyond graph energy: Norms of graphs and matrices, Linear Algebra Appl. 506 (2016), 82–138. https://doi.org/10.1016/j.laa.2016.05.011

[26] S. Pirzada, B.A. Rather, and M. Aouchiche, On eigenvalues and energy of geometric–arithmetic matrix of graphs, Medit. J. Math. 19 (2022), no. 3, Article number: 115. https://doi.org/10.1007/s00009-022-02035-0

[27] M. Randić, Characterization of molecular branching, J. Am. Chem. Soc. 97 (1975), no. 23, 6609–6615. https://doi.org/10.1021/ja00856a001

[28] M. Randić, Topological indices, Encyclopedia of Computational Chemistry (P.V.R. Schleye, ed.), Wiley, London, 1998, pp. 3018–3032.

[29] M. Randić, On generalization of Wiener index for cyclic structures, Acta Chim. Slov. 49 (2002), no. 3, 483–496.

[30] B.A. Rather, M. Aouchiche, M. Imran, and S. Pirzada, On arithmetic–geometric eigenvalues of graphs, Main Group Metal Chem. 45 (2022), no. 1, 111–123. https://doi.org/10.1515/mgmc-2022-0013

[31] B.A. Rather, M. Aouchiche, and S. Pirzada, Spread of geometric-arithmetic matrix of graphs, AKCE Int. J. Graphs Comb. 19 (2022), no. 2, 146–153.  https://doi.org/10.1080/09728600.2022.2088315

[32] J.M. Rodríguez and J.M. Sigarreta, Spectral study of the geometric-arithmetic index, MATCH Commun. Math. Comput. Chem. 74 (2015), no. 1, 121–135.

[33] J.M. Rodríguez and J.M. Sigarreta, Spectral properties of geometric–arithmetic index, Appl. Math. Comp. 277 (2016), 142–153.  https://doi.org/10.1016/j.amc.2015.12.046

[34] G. Rücker and C. Rücker, On topological indices, boiling points, and cycloalkanes, J. Chem. Inf. Comput. Sci. 39 (1999), no. 5, 788–802.  https://doi.org/10.1021/ci9900175

[35] Y. Shao and Y. Gao, The maximal geometric-arithmetic energy of trees with at most two branched vertices, Appl. Math. Comp. 362 (2019), 124528.  https://doi.org/10.1016/j.amc.2019.06.042

[36] M. Sohrabi-Haghighat and M. Rostami, Using linear programming to find the extremal graphs with minimum degree 1 with respect to geometric-arithmetic index, Appl. math. Eng. Manag. Tec. 3 (2015), no. 1, 534–539.

[37] R. Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics, Wiley-VCH, Weinheim, 2009.

[38] S. Vujošević, G. Popivoda, Ž.K. Vukićević, B. Furtula, and R. Škrekovski, Arithmetic–geometric index and its relations with geometric–arithmetic index, Appl. Math. Comp. 391 (2021), 125706. https://doi.org/10.1016/j.amc.2020.125706

[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 (2009), no. 4, 1369–1376. https://doi.org/10.1007/s10910-009-9520-x

[40] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947), no. 1, 17–20. https://doi.org/10.1021/ja01193a005

[41] Y. Yuan, B. Zhou, and N. Trinajstić, On geometric-arithmetic index, J. Math. Chem. 47 (2010), no. 2, 833–841. https://doi.org/10.1007/s10910-009-9603-8

[42] X. Zhao, Y. Shao, and Y. Gao, The maximal geometric-arithmetic energy of trees, MATCH Commun. Math. Comput. Chem. 84 (2020), no. 2, 363–367.