Acknowledgement
The authors are grateful to the anonymous referees, Editor-in-Chief (Prof. Jung Yoog Kang) for their careful reading, valuable comments and helpful suggestions, which have helped to improve the presentation of this work significantly.
References
- S. Akhter, R. Farooq, Eccentric adjacency index of graphs with a given number of cut edges, B. Malays. Math. Sci. So. 43 (2020), 2509-2522. https://doi.org/10.1007/s40840-019-00820-x
- M. Azari, A. Iranmanesh, Some inequalities for the multiplicative sum Zagreb index of graph operations, J. Math. Inequal. 9 (2015), 727-738.
- B. Basavanagoud, S. Patil, Multiplicative Zagreb indices and coindices of some derived graphs, Opuscula Math. 36 (2016), 287-299. https://doi.org/10.7494/opmath.2016.36.3.287
- J.A. Bondy, U.S.R. Murty, Graph Theory with Applications, Elsevier, New York, 1976.
- Bozovic, Z.K. Kovijanic, G. Popivoda, Chemical trees with extreme values of a few types of multiplicative Zagreb indices, MATCH Commun. Math. Comput. Chem. 76 (2016), 207-220.
- S. Chen, W. Liu, Extremal Zagreb indices of graphs with a given number of cut edges, Graphs Comb. 30 (2014), 109-118. https://doi.org/10.1007/s00373-012-1258-8
- J. Du, X. Sun, On the multiplicative sum Zagreb index of graphs with some given parameters, J. Math. Inequal. 14 (2020), 1165-1181.
- M. Eliasi, A. Iranmanesh, I. Gutman, Multiplicative versions of first Zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012), 217-230.
- K. Fang, J. Shu, On graphs with cut vertices and cut edges, Acta Math. Sin. 30 (2014), 539-546. https://doi.org/10.1007/s10114-014-1230-z
- Y. Feng, X. Hu, S. Li, On the extremal Zagreb indices of graphs with cut edges, Acta Appl. Math. 110 (2010), 667-684. https://doi.org/10.1007/s10440-009-9467-8
- I. Gutman, Degree-based topological indices, Croat. Chem. Acta 86 (2013), 351-361. https://doi.org/10.5562/cca2294
- I. Gutman, B. Furtula, Novel Molecular Structure Descriptors-Theory and Applications I, Kragujevac Univ., Kragujevac, 2010.
- I. Gutman, B. Furtula, Novel Molecular Structure Descriptors-Theory and Applications II, Kragujevac Univ., Kragujevac, 2010.
- I. Gutman, N. Trinajsti'c, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535-538. https://doi.org/10.1016/0009-2614(72)85099-1
- X. He, S. Li, Q. Zhao, Sharp bounds on the reduced second Zagreb index of graphs with given number of cut vertices, Discrete Appl. Math. 271 (2019), 49-63. https://doi.org/10.1016/j.dam.2019.08.014
- X. Li, Y. Fan, The connectivity and the Harary index of a graph, Discret. Appl. Math. 181 (2015), 167-173. https://doi.org/10.1016/j.dam.2014.08.022
- G. Su, L. Xiong, L. Xu, B. Ma, On the maximum and minimum first reformulated Zagreb index of graphs with connectivity at most k, Filomat 25 (2011), 75-83. https://doi.org/10.2298/FIL1104075S
- R. Todeschini, V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000.
- R. Todeschini, V. Consonni, New local vertex invariants and molecular descriptors based on functions of the vertex degrees, MATCH Commun. Math. Comput. Chem. 64 (2010), 359-372.
- H. Wang, S. Wang, B. Wei, Sharp bounds for the modified multiplicative Zagreb indices of graphs with vertex connectivity at most k, Filomat 33 (2019), 4673-4685. https://doi.org/10.2298/fil1914673w
- R. Wu, H. Chen, H. Deng, On the monotonicity of topological indices and the connectivity of a graph, Appl. Math. Comput. 298 (2017), 188-200. https://doi.org/10.1016/j.amc.2016.11.017
- K. Xu, K.C. Das, Trees, unicyclic, and bicyclic graphs extremal with respect to multiplicative sum Zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012), 257-272.
- Q. Zhao, S. Li, On the maximum Zagreb indices of graphs with k cut vertices, Acta Appl. Math. 111 (2010), 93-106. https://doi.org/10.1007/s10440-009-9534-1