Zeroth-order general Randi´c index of trees
DOI:
https://doi.org/10.5269/bspm.45062Abstract
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.
References
1. 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).
2. 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
3. Das, K. C., Xu, K., Gutman, I., On Zagreb and Harary indices. MATCH Commun. Math. Comput. Chem. 70 (1), 301-314, (2013).
4. 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).
5. Hao, J., Relationship between modified Zagreb indices and reformulated modified Zagreb indices with respect to trees. Ars Combin. 121, 201-206, (2015).
6. 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
7. 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
8. 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).
9. 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).
10. 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).
11. 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
12. 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).
2. 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
3. Das, K. C., Xu, K., Gutman, I., On Zagreb and Harary indices. MATCH Commun. Math. Comput. Chem. 70 (1), 301-314, (2013).
4. 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).
5. Hao, J., Relationship between modified Zagreb indices and reformulated modified Zagreb indices with respect to trees. Ars Combin. 121, 201-206, (2015).
6. 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
7. 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
8. 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).
9. 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).
10. 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).
11. 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
12. 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).
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2022-01-23
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