[1] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Springer, New York, 2008.
[2] O. Ivanciuc, T. S. Balaban and A. T. Balaban, Design of topological indices. Part 4. Reciprocal distance matrix, related lacal vertex invariants and topological indices, J. Math. Chem. 12 (1993) 309–318, https://doi.org/10.1007/BF01164642.
[3] D. Plavšic, S. Nikolic, N. Trinajstic and Z. Mihalic, On the Harary index for the characterization of chemical graphs, J. Math. Chem. 12 (1993) 235–250, https://doi.org/10.1007/BF01164638.
[4] 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.
[5] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015) 1184–1190, https://doi.org/10.1007/s10910-015-0480-z.
[6] Y. Alizadeh, A. Iranmanesh and T. Došlic, Additively weighted Harary index of some composite graphs, Discrete Math. 313 (2013) 26–34, https://doi.org/10.1016/j.disc.2012.09.011.
[7] R. Li, Harary index and some Hamiltonian properties of graphs, AKCE Int. J. Graphs Comb. 12 (2015) 64–69, https://doi.org/10.1016/j.akcej.2015.06.010.
[8] V. Sharma, R. Goswami and A. K. Madan, Eccentric connectivity index: a novel highly discriminating topological descriptor for structure property and structure activity studies, J. Chem. Inf. Comput. Sci. 37 (1997) 273–282, https://doi.org/10.1021/ci960049h.
[9] S. Gupta, M. Singh and A. K. Madan, Eccentric distance sum: a novel graph invariant for predicting biological and physical properties, J. Math. Anal. Appl. 275 (2002) 386–401, https://doi.org/10.1016/S0022-247X(02)00373-6.
[10] S. Gupta, M. Singh and A. K. Madan, Connective eccentricity index: a novel topological descriptor for predicting biological activity, J. Mol. Graph. Model. 18 (2000) 18–25, https://doi.org/10.1016/S1093-3263(00)00027-9.
[11] H. -S. Lim, H. -C. Kim and J. -H. Park, Ore-type degree conditions for disjoint path covers in simple graphs, Discrete Math. 339 (2016) 770–779, https://doi.org/10.1016/j.disc.2015.10.021.
[12] C. -K. Lin, Y. -H. Teng, J. J. M. Tan, L. -H. Hsu and D. Marušic, The spanning laceability on the faulty bipartite hypercube-like networks, Appl. Math. Comput. 219 (2013) 8095–8103, https://doi.org/10.1016/j.amc.2013.02.027.
[13] L. Donati, S. Chewle, D. S. Pierre, V. Natarajan and M. Weber, Topological analysis reveals multiple pathways in molecular dynamics, J. Chem. Theory Comput. 21 (2025) 10385–10397, https://doi.org/10.1021/acs.jctc.5c00819.
[14] J. L. Andersen, R. Fagerberg, C. Flamm, W. Fontana, J. Kolcák, C. V. Laurent, D. Merkle and N. Nøjgaard, Graph transformation for enzymatic mechanisms, Bioinformatics 37 (2021) 392–400, https://doi.org/10.1093/bioinformatics/btab296.
[15] W. D. Jang, G. B. Kim, Y. Kim and S. Y. Lee, Applications of artificial intelligence to enzyme and pathway design for metabolic engineering, Curr. Opin. Biotechnol. 73 (2022) 101–107,
https://doi.org/10.1016/j.copbio.2021.07.024.
[16] Y. -Y. Liu and A. -L. Barabási, Control principles of complex systems, Rev. Mod. Phys. 88 (2016) #035006, https://doi.org/10.1103/RevModPhys.88.035006.
[17] H. Hua and M. Wang, On Harary index and traceable graphs, MATCH Commun. Math. Comput. Chem. 70 (2013) 297–300.
[18] H. Hua and B. Ning, Wiener index, Harary index and Hamiltonicity of graphs, MATCH Commun. Math. Comput. Chem. 78 (2017) 153–162.
[19] R. Liu, X. Du and H. Jia, Some observations on Harary index and traceable graphs, MATCH Commun. Math. Comput. Chem. 77 (2017) 195–208.
[20] Q. Zhou, L. Wang and Y. Lu, Wiener index and Harary index on Hamiltonconnected graphs with large minimum degree, Discrete Appl. Math. 247 (2018) 180–185, https://doi.org/10.1016/j.dam.2018.03.063.
[21] M. An, The first Zagreb index, reciprocal degree distance and Hamiltonian-connectedness of graphs, Inform. Process. Lett. 176 (2022) #106247, https://doi.org/10.1016/j.ipl.2022.106247.
[22] M. An and K. C. Das, First Zagreb index, k-connectivity, -deficiency and k-Hamiltonicity of graphs, MATCH Commun. Math. Comput. Chem. 80 (2018) 141–151.
[23] R. Kori, A. Prasad and A. K. Upadhyay, Reciprocal degree distance and Hamiltonian properties of graphs, Oper. Res. Lett. 51 (2023) 623–627.
[24] X. Zhu, L. Feng, M. Liu, W. Liu and Y. Hu, Some topological indices and graph properties, Trans. Comb. 6 (2017) 51–65.
[25] M. An, Y. Zhang and H. Yan, Sufficient conditions for k-leaf-connected graphs in terms of the first Zagreb index, the reciprocal degree distance and the forgotten topological index, Discrete Appl. Math. 351 (2024) 74–80, https://doi.org/10.1016/j.dam.2024.03.008.
[26] H. Liu, L. You, H. Hua and Z. Du, Some sufficient conditions for graphs to be k-leafconnected, Discrete Appl. Math. 352 (2024) 1–8, https://doi.org/10.1016/j.dam.2024.03.017.
[27] L. -H. Hsu and C. -K. Lin, Graph Theory and Interconnection Networks, CRC Press, 2008.
[28] C. -K. Lin, J. J. M. Tan, D. F. Hsu and L. -H. Hsu, On the spanning fan-connectivity of graphs, Discrete Appl. Math. 157 (2009) 1342–1348, https://doi.org/10.1016/j.dam.2008.11.014.
[29] E. Sabir and J. Meng, Degree sequence conditions for a graph to be disjoint path coverable, Discrete Appl. Math. 332 (2023) 62–69, https://doi.org/10.1016/j.dam.2023.02.002.
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