Zeroth-order general Randi´c index of trees
Resumo
Randi\'{c} indices belong to the most well-known topological indices. We study a very general index called the zeroth-order general Randi\'{c} index. We present upper and lower bounds on the zeroth-order general Randi\'{c} index for trees with given order and independence number, and for trees with given order and domination number. We also show that the bounds are best possible.
Downloads
Referências
Akhter, N., Jamil, M. K., Tomescu, I., Extremal first and second Zagreb indices of apex trees. U. P. B. Sci. Bull. Series A 78 (4), 221-230, (2016).
Borovicanin, B., Furtula, B., On extremal Zagreb indices of trees with given domination number. Appl. Math. Comput. 279, 208-218, (2016). https://doi.org/10.1016/j.amc.2016.01.017
Das, K. C., Xu, K., Gutman, I., On Zagreb and Harary indices. MATCH Commun. Math. Comput. Chem. 70 (1), 301-314, (2013).
Deng, H., A unified approach to the extremal Zagreb indices for trees, unicyclic graphs and bicyclic graphs. MATCH Commun. Math. Comput. Chem. 57 (3), 597-616, (2007).
Hao, J., Relationship between modified Zagreb indices and reformulated modified Zagreb indices with respect to trees. Ars Combin. 121, 201-206, (2015).
Kazemi, R., Behtoei, A., The first Zagreb and forgotten topological indices of d-ary trees. Hacet. J. Math. Stat. 46 (4), 603-611, (2017). https://doi.org/10.15672/HJMS.20174622758
Khalid, S., Ali, A., On the zeroth-order general Randic index, variable sum exdeg index and trees having vertices with prescribed degree. Discrete Math. Algorithms Appl. 10 (2), 1850015, (2018). https://doi.org/10.1142/S1793830918500155
Lin, H., On segments, vertices of degree two and the first Zagreb index of trees. MATCH Commun. Math. Comput. Chem. 72 (3), 825-834, (2014).
Tomescu, I., Jamil, M. K., Maximum general sum-connectivity index for trees with given independence number. MATCH Commun. Math. Comput. Chem. 72 (3), 715-722, (2014).
Vasilyev, A., Darda, R., Stevanovic, D., Trees of given order and independence number with minimal first Zagreb index. MATCH Commun. Math. Comput. Chem. 72 (3), 775-782, (2014).
Vetrık, T., Balachandran, S., General multiplicative Zagreb indices of trees. Discrete Appl. Math. 247, 341-351, (2018). https://doi.org/10.1016/j.dam.2018.03.084
Yamaguchi, S., Zeroth-order general Randic index of trees with given order and distance conditions. MATCH Commun. Math. Comput. Chem. 62 (1), 171-175, (2009).
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
