Harmonic index and harmonic polynomial of some chemical graphs

[1] N. Bukhary, Domination in Benzenoids, Master’s thesis, Virginia Commonwealth University, Richmond, Virginia, United States., 2010.

[2] W. Carballosa, J.E. N´apoles, J. Rodr´ıguez, O. Rosario, and J. Sigarreta, Mathematical results on harmonic polynomials, Commun. Comb. Optim. 9 (2024), no. 2, 279–295.  https://doi.org/10.22049/cco.2023.28920.1779

[3] H. Deng, S. Balachandran, S.K. Ayyaswamy, and Y.B. Venkatakrishnan, On the harmonic index and the chromatic number of a graph, Discrete Appl. Math. 161 (2013), no. 16-17, 2740–2744. https://doi.org/10.1016/j.dam.2013.04.003

[4] S. Fajtlowicz, On conjectures of Graffiti-II, Congr. Numer. 60 (1987), 187–197.

[5] W. Gao, M.K. Siddiqui, M. Imran, M.K. Jamil, and M.R. Farahani, Forgotten topological index of chemical structure in drugs, Saudi Pharm J. 24 (2016), no. 3, 258–264.  https://doi.org/10.1016/j.jsps.2016.04.012

[6] J.C. Hernández-Gómez, J.A. Méndez-Berm´udez, J.M. Rodríguez, and J.M. Sigarreta, Harmonic index and harmonic polynomial on graph operations, Symmetry 10 (2018), no. 10, 456. https://doi.org/10.3390/sym10100456

[7] S. Hosamani, D. Perigidad, S. Jamagoud, Y. Maled, and S. Gavade, Qspr analysis of certain degree based topological indices, J. Stat. Appl. Probab. 6 (2017), no. 2, 361–371.  http://doi.org/10.18576/jsap/060211

[8] M.A. Iranmanesh and M. Saheli, On the harmonic index and harmonic polynomial of caterpillars with diameter four, Iran. J. Math. Chem. 6 (2015), no. 1, 41–49.  https://doi.org/10.22052/ijmc.2015.9044

[9] J. Li and W.C. Shiu, The harmonic index of a graph, Rocky Mountain J. Math. 44 (2014), no. 5, 1607–1620.

[10] J.B. Lv and J. Li, On the harmonic index and the matching number of a tree., Ars Combin. 116 (2014), 407–416.

[11] M. Pumera, A. Ambrosi, A. Bonanni, E.L.K. Chng, and H.L. Poh, Graphene for electrochemical sensing and biosensing, TrAC-Trends Anal. Chem. 29 (2010), no. 9, 954–965.  https://doi.org/10.1016/j.trac.2010.05.011

[12] L. Wang, Y. Zhang, J. Tian, H. Li, and X. Sun, Conjugation polymer nanobelts: a novel fluorescent sensing platform for nucleic acid detection, Nucleic Acids Res. 39 (2011), no. 6, e37.  https://doi.org/10.1093/nar/gkq1294

[13] L. Yang and H. Hua, The harmonic index of general graphs, nanocones and triangular benzenoid graphs, Optoelectron. Adv. Mat. 6 (2012), no. 5–6, 660–663.

[14] Y. Zuo, Y. Tang, and H.Y. Deng, The extremal graphs for (sum-) balaban index of spiro and polyphenyl hexagonal chains, Iran. J. Math. Chem. 9 (2018), no. 4,  241–254.  https://doi.org/10.22052/ijmc.2018.143823.1381