A survey on symmetric division degree index

[1] H. Abdo, D. Dimitrov, The total irregularity of graphs under graph operations, Miskolc Math.

Notes 15 (2014) 3–17.

[2] A. M. Albalahi, A. Ali, On the Maximum Symmetric Division Deg Index of k-Cyclic Graphs, J.

Math. 2022 (2022).

[3] A. Ali, S. Elumalai, T. Mansour, On the symmetric division deg index of molecular graphs,

MATCH Commun. Math. Comput. Chem. 83 (2020) 205–220.

[4] K. C. Das, M. Matej´c, E. Milovanovi´c, I. Milovanovi´c, Bounds for symmetric division deg index of graphs, Filomat 33(3) (2019) 683–698.

[5] J. Devillers, A. T. Balaban (Eds.), Topological Indices and Related Descriptors in QSAR and QSPR,

Gordon and Breach, Amsterdam, 1999.

[6] J. Du, X. Sun, On symmetric division deg index of trees with given parameters, AIMS Math. 6(6)

(2021) 6528–6541.

 [7] M. Eliasi, A. Iranmanesh, I. Gutman, Multiplicative versions of first Zagreb index, MATCH Commun. Math. Comput. Chem. 68(1) (2012) 217–230.

[8] E. Estrada, Atom-bond connectivity and the energetic of branched alkanes, Chem. Phys. Lett. 463 (2008) 422–425.

[9] E. Estrada, L. Torres, L. Rodriguez, I. Gutman, An atom-bond connectivity index: Modelling the

enthalpy of formation of alkanes, Indian J. Chem. 37 A (1998) 849–855.

[10] S. Fajtlowicz, On conjectures of graffiti II, Congr. Numer. 60 (1987) 189–197.

[11] B. Furtula, K. Das, I. Gutman, Comparative analysis of symmetric division deg index as potentially useful molecular descriptor, Int. J. Quantum Chem. 118 (2018) 25659.

[12] B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015) 1184–1190.

[13] Y. J. Ge, J. B. Liu, M. Younas, M. Yousaf, W. Nazeer, Analysis of SC5C7[p, q] and NPHX[p, q] nanotubes via topological indices, J. Nanomater. 2019 (2019) 1–10.

[14] M. Ghorbani, S. Zangi, N. Amraei, New results on symmetric division deg index, J. Appl. Math.

Comput. 65 (2021) 161–176.

[15] C. K. Gupta, V. Lokesha, S. B. Shwetha, On the symmetric division deg index of graph, Southeast Asian Bull. Math. 40 (2016) 59–80.

[16] I. Gutman, Multiplicative Zagreb indices of trees, Bull. Int. Math. Virt. Inst. 1 (2011) 13–19.

[17] I. Gutman, B. Ruˇsˇci´c, N. Trinajsti´c, C. F. Wilcox, Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys. 62 (1975) 3399–3405.

[18] I. Gutman, M. Togan, A. Yurttas, A. S. CEVIK, I. N. CANGUL, Inverse Problem for Sigma Index,

MATCH Commun. Math. Comput. Chem. 79(2) (2018) 491–508.

[19] I. Gutman, N. Trinajsti´c, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538.

[20] G. O. Kizilirmak, E. Sevgi, S. Buyukkose, I. N. Cangul, Lower and Upper Bounds for Some Degree-Based Indices of Graphs, Preprints 2022, 2022110152 (doi: 10.20944/preprints202211.0152.v1).

[21] D. J. Klein, M. Randi´c, Resistance distance, J. Math. Chem. 12 (1993) 81–95.

[22] H. Liu, Y. Huang, Sharp bounds on the symmetric division deg index of graphs and line graphs, Comp. Appl. Math. 42(6) (2023) 285.

[23] C. Liu, Y. Pan, J. Li, tricyclic graphs with the minimum symmetric division deg index, Discrete

Math. Lett. 3 (2020) 14–18.

[24] V. Lokesha, T. Deepika, Symmetric division deg index of tricyclic and tetracyclic graphs, Int. J. Sci. Eng. Res. 7(5) (2016) 53–55.

[25] V. Lokesha, T. Deepika, I. N. Cangul, Symmetric division deg and inverse sum indeg indices of

polycyclic aromatic hydrocarbons (PAHs) and poly-hex nanotubes, Southeast Asian Bull. Math.

41 (2017) 707–715.

[26] I. Zˇ . Milovanovic´, E. I. Milovanovic´, I. Gutman, B. Furtula, Some inequalities for the forgotten

topological index, Int. J. Appl. Graph Theory 1(1) (2017) 1–15

[27] G. Mohanappriya, D. Vijayalakshmi, Symmetric division degree index and inverse sum index of

transformation graph, J. Phys.: Conf. Ser. 1139 (2018) 012048.

[28] M. Munir,W. Nazeer, A. R. Nizami, S. Rafique, S. M. Kang, M-polynomials and topological indices of titania nanotubes, Symmetry 8(11) (2016) 1–9.

[29] J. L. Palacios, New upper bounds for the symmetric division deg index of graphs, Discrete Math. Lett. 2 (2019) 52–56.

[30] Y. Pan, J. Li, Graphs that minimizing symmetric division deg index, MATCH Commun. Math.

Comput. Chem. 82 (2019) 43–55.

[31] A. Rajpoot, L. Selvaganesh, Bounds of the Symmetric Division Deg Index for Trees and Unicyclic Graphs with A Perfect Matching, Iranian J. Math. Chem. 11(3) (2020) 141–159

[32] A. Rajpoot, L. Selvaganesh, Study of Bounds and Extremal Graphs of Symmetric Division Degree Index for Bicyclic Graphs with Perfect Matching, Iranian J. Math. Chem. 13(2) (2022) 145–165

[33] M. Randi´c, On characterization of molecular branching, J. Am. Chem. Soc. 97 (1975) 6609–6615.

[34] Y. Rao, A. Kanwal, R. Abbas, S. Noureen, A. Fahad, M. Qureshi, Some degree-based topological indices of caboxy-terminated dendritic macromolecule, Main Group Met. Chem. 44(1) (2021) 165-172.

[35] G.H. Shirdel, H. Rezapour, A.M. Sayadi, The Hyper-Zagreb index of graph operations, Iran. J.

Math. Chem. 4(2) (2013) 213–220.

 [36] X. Sun, Y. Gao, J. Du, On symmetric division deg index of unicyclic graphs and bicyclic graphs

with given matching number, AIMS Math. 6(8) (2021) 9020–9035.

[37] A. Vasilyev, Upper and lower bounds of symmetric division deg index, Iran. J. Math. Chem. 2

(2014) 91–98.

[38] D. Vukiˇcevi´c, Bond additive modeling 2. Mathematical properties of max-min rodeg index, Croat. Chem. Acta 83 (2010) 261–273.

[39] D. Vukiˇcevi´c, M. Gaˇsperov, Bond additive modeling 1. Adriatic indices, Croat. Chem. Acta 83

(2010) 243–260.

[40] B. Yang, V. V. Manjalapur, S. P. Sajjan, M. M. Matthai, J. B. Liu, On extended adjacency index with respect to acyclic, unicyclic and bicyclic graphs, Mathematics 7(7) (2019) 652.