Extremal trees and molecular trees with respect to the Sombor-index-like graph invariants and
Czechoslovak Mathematical Journal (2024)
- Volume: 74, Issue: 3, page 927-941
- ISSN: 0011-4642
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topGao, Wei. "Extremal trees and molecular trees with respect to the Sombor-index-like graph invariants $\mathcal {SO}_5$ and $\mathcal {SO}_6$." Czechoslovak Mathematical Journal 74.3 (2024): 927-941. <http://eudml.org/doc/299311>.
@article{Gao2024,
abstract = {I. Gutman (2022) constructed six new graph invariants based on geometric parameters, and named them Sombor-index-like graph invariants, denoted by $\mathcal \{SO\}_1, \mathcal \{SO\}_2, \dots , \mathcal \{SO\}_6$. Z. Tang, H. Deng (2022) and Z. Tang, Q. Li, H. Deng (2023) investigated the chemical applicability and extremal values of these Sombor-index-like graph invariants, and raised some open problems, see Z. Tang, Q. Li, H. Deng (2023). We consider the first open problem formulated at the end of Z. Tang, Q. Li, H. Deng (2023). We obtain the extremal values of the graph invariants $\mathcal \{SO\}_5$ and $\mathcal \{SO\}_6$ among all trees and molecular trees of order $n$, and characterize the trees and molecular trees that achieve the extremal values, respectively. Thus, the problem is completely solved.},
author = {Gao, Wei},
journal = {Czechoslovak Mathematical Journal},
keywords = {tree; molecular tree; Sombor-index-like graph invariant; extremal value},
language = {eng},
number = {3},
pages = {927-941},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extremal trees and molecular trees with respect to the Sombor-index-like graph invariants $\mathcal \{SO\}_5$ and $\mathcal \{SO\}_6$},
url = {http://eudml.org/doc/299311},
volume = {74},
year = {2024},
}
TY - JOUR
AU - Gao, Wei
TI - Extremal trees and molecular trees with respect to the Sombor-index-like graph invariants $\mathcal {SO}_5$ and $\mathcal {SO}_6$
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 3
SP - 927
EP - 941
AB - I. Gutman (2022) constructed six new graph invariants based on geometric parameters, and named them Sombor-index-like graph invariants, denoted by $\mathcal {SO}_1, \mathcal {SO}_2, \dots , \mathcal {SO}_6$. Z. Tang, H. Deng (2022) and Z. Tang, Q. Li, H. Deng (2023) investigated the chemical applicability and extremal values of these Sombor-index-like graph invariants, and raised some open problems, see Z. Tang, Q. Li, H. Deng (2023). We consider the first open problem formulated at the end of Z. Tang, Q. Li, H. Deng (2023). We obtain the extremal values of the graph invariants $\mathcal {SO}_5$ and $\mathcal {SO}_6$ among all trees and molecular trees of order $n$, and characterize the trees and molecular trees that achieve the extremal values, respectively. Thus, the problem is completely solved.
LA - eng
KW - tree; molecular tree; Sombor-index-like graph invariant; extremal value
UR - http://eudml.org/doc/299311
ER -
References
top- Gutman, I., Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), 11-16. (2021) Zbl1474.92154MR4773882
- Gutman, I., 10.30538/psrp-odam2022.0072, Open J. Discr. Appl. Math. 5 (2022), 1-5. (2022) MR4471690DOI10.30538/psrp-odam2022.0072
- Gutman, I., Miljković, O., Molecules with smallest connectivity indices, MATCH Commun. Math. Comput. Chem. 41 (2000), 57-70. (2000) Zbl1036.92043MR1787632
- Tang, Z., Deng, H., 10.48550/arXiv.2208.09154, Available at https://arxiv.org/abs/2208.09154 (2022), 9 pages. (2022) DOI10.48550/arXiv.2208.09154
- Tang, Z., Li, Q., Deng, H., 10.46793/match.90-1.203T, MATCH Commun. Math. Comput. Chem. 90 (2023), 203-222. (2023) Zbl1519.92356MR4767035DOI10.46793/match.90-1.203T
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