Multiplicative Zagreb indices of trees with given domination number

Document Type : Short notes

Authors

1 University of the Free State

2 Slovak University of Technology

Abstract

In [On extremal multiplicative Zagreb indices of trees with given domination number, Applied Mathematics and Computation 332 (2018), 338--350] Wang et al. presented bounds on the multiplicative Zagreb indices of trees with given domination number. We fill in the gaps in their proofs of Theorems 3.1 and 3.3 and we correct Theorem 3.3.

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Main Subjects


[1] Z.H. Ahsan and S.H. Arshad, Computing multiplicative topological indices of some chemical nenotubes and networks, Open J. Discrete Appl. Math. 2 (2019), no. 3, 7–18.
[2] B. Borovićanin and B. Furtula, On extremal Zagreb indices of trees with given domination number, Appl. Math. Comput. 279 (2016), 208–218.
https://doi.org/10.1016/j.amc.2016.01.017
[3] A. Javed, M.K. Jamil, J.B. Liu, and A. Ali, Extremal (n, m)-graphs w.r.t. general multiplicative Zagreb indices, Comb. Chem. High Throughput Screen. 25 (2022), no. 3, 476–482.
http://doi.org/10.2174/1386207323999201103222640
[4] R. Kazemi, Note on the multiplicative Zagreb indices, Discrete Appl. Math. 198 (2016), 147–154.
https://doi.org/10.1016/j.dam.2015.06.028
[5] J.V. Kureethara, A. Asok, and I.N. Cangul, Inverse problem for the forgotten and the hyper Zagreb indices of trees, Commun. Comb. Optim. 7 (2022), no. 2, 203–209.
https://doi.org/10.22049/cco.2021.27034.1182
[6] I. Milovanović, M. Matejić, E. Milovanović, and R. Khoeilar, A note on the first Zagreb index and coindex of graphs, Commun. Comb. Optim. 6 (2021), no. 1, 41–51.
https://doi.org/10.22049/cco.2020.26809.1144
[7] F.F. Nezhad, A. Iranmanesh, A. Tehranian, and M. Azari, Strict lower bounds on the multiplicative Zagreb indices of graph operations., Ars Combin. 117 (2014), 399–409.
[8] T. Vetrík and S. Balachandran, General multiplicative Zagreb indices of trees, Discrete Appl. Math. 247 (2018), 341–351.
https://doi.org/10.1016/j.dam.2018.03.084
[9] S. Wang, C. Wang, and J.B. Liu, On extremal multiplicative Zagreb indices of trees with given domination number, Applied Math. Comput. 332 (2018), 338–350.
https://doi.org/10.1016/j.amc.2018.03.058
[10] K. Xu and H. Hua, A unified approach to extremal multiplicative Zagreb indices for trees, unicyclic and bicyclic graphs, MATCH Commun. Math. Comput. Chem. 68 (2012), no. 1, 241–256.