Geodesic
Extremal values on the modified Sombor index of trees and unicyclic graphs
Ural mathematical journal, Tome 10 (2024) no. 1, pp. 68-75 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $G=(V,E)$ be a simple connected graph. The modified Sombor index denoted by $mSo(G)$ is defined as $$mSo(G)=\sum_{uv\in E}\frac{1}{\sqrt{d^2_u+d^2_v}},$$ where $d_v$ denotes the degree of vertex $v$. In this paper we present extremal values of modified Sombor index over the set of trees and unicyclic graphs.
Keywords: Modified Sombor Index, Trees, Unicyclic graphs, Extremal values 
@article{UMJ_2024_10_1_a5,
     author = {Raghavendra H. Kashyap and Yanamandram B. Venkatakrishnan and Rashad Ismail and Selvaraj Balachandran and Hari Naresh Kumar},
     title = {Extremal values on the modified {Sombor} index of trees and unicyclic graphs},
     journal = {Ural mathematical journal},
     pages = {68--75},
     year = {2024},
     volume = {10},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2024_10_1_a5/}
}
TY  - JOUR
AU  - Raghavendra H. Kashyap
AU  - Yanamandram B. Venkatakrishnan
AU  - Rashad Ismail
AU  - Selvaraj Balachandran
AU  - Hari Naresh Kumar
TI  - Extremal values on the modified Sombor index of trees and unicyclic graphs
JO  - Ural mathematical journal
PY  - 2024
SP  - 68
EP  - 75
VL  - 10
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UMJ_2024_10_1_a5/
LA  - en
ID  - UMJ_2024_10_1_a5
ER  - 
%0 Journal Article
%A Raghavendra H. Kashyap
%A Yanamandram B. Venkatakrishnan
%A Rashad Ismail
%A Selvaraj Balachandran
%A Hari Naresh Kumar
%T Extremal values on the modified Sombor index of trees and unicyclic graphs
%J Ural mathematical journal
%D 2024
%P 68-75
%V 10
%N 1
%U http://geodesic.mathdoc.fr/item/UMJ_2024_10_1_a5/
%G en
%F UMJ_2024_10_1_a5
Raghavendra H. Kashyap; Yanamandram B. Venkatakrishnan; Rashad Ismail; Selvaraj Balachandran; Hari Naresh Kumar. Extremal values on the modified Sombor index of trees and unicyclic graphs. Ural mathematical journal, Tome 10 (2024) no. 1, pp. 68-75. http://geodesic.mathdoc.fr/item/UMJ_2024_10_1_a5/

[1] Cruz R., Gutman I., Rada J., “Sombor index of chemical graphs”, Appl. Math. Comput., 399 (2021), 126018 | DOI | MR | Zbl

[2] Cruz R., Rada J., “The path and the star as extremal values of vertex-degree-based topological indices among trees”, MATCH Commun. Math. Comput. Chem., 82 (2019), 715–732 | MR | Zbl

[3] Deng H., Tang Z., Wu R., “Molecular trees with extremal values of Sombor indices”, Int. J. Quantum Chem., 121:11 (2021), 26622 | DOI

[4] Gutman I., “Geometric approach to degree-based topological indices: Sombor indices.”, MATCH Commun. Math. Comput. Chem., 86 (2021), 11–16 | MR | Zbl

[5] Gutman I., Redžepović I., Furtula B., “On the product of Sombor and modified Sombor indices”, Open J. Discrete Appl. Math., 6:2 (2023), 1–6. | DOI | MR

[6] Hernández J. C., Rodríguez J. M., Rosario O., Sigarreta J. M., “Extremal problems on the general Sombor index of a graph”, AIMS Mathematics, 7:5 (2022), 8330–8343 | DOI | MR

[7] Huang Y., Liu H., “Bounds of modified Sombor index, spectral radius and energy”, AIMS Mathematics, 6:10 (2021), 11263–11274 | DOI | MR | Zbl

[8] Shooshtari H., Sheikholeslami S. M., Amjadi J., “Modified Sombor index of unicyclic graphs with a given diameter”, Asian-Eur. J. Math., 16:06 (2023), 2350098 | DOI | MR

[9] Wu F., An X., Wu B., “Sombor indices of cacti”, AIMS Mathematics, 8:1 (2023), 1550–1565 | DOI | MR

[10] Yang Ch., Ji M., Das K.C., Mao Y., “Extreme graphs on the Sombor indices”, AIMS Mathematics, 7:10 (2022), 19126–19146 | DOI | MR

[11] Zuo X., Rather B. A., Imran M., Ali A., “On some topological indices defined via the modified Sombor matrix”, Molecules, 27:19 (2022), 6772 | DOI