The Sombor spectral radius 
of a graph is defined as the largest eigenvalue
of the Sombor matrix.
Liu et al. (2022) shows that for any tree,
 |
with equality iff the tree is the star graph 
(Zheng et al. 2023).
Sombor Spectral Radius
See also
Sombor Matrix, Graph Eigenvalue, Spectral RadiusExplore with Wolfram|Alpha
References
Guo, X. and Gao, Y. "Arithmetic-Geometric Spectral Radius and Energy of Graphs." MATCH Commun. Math. Comput. Chem. 83, 651-680, 2020.Gutman, I. "Geometric Approach to Degree-Based Topological Indices: Sombor Indices." MATCH Commun. Math. Comput. Chem. 86, 11-16, 2021.Gutman, I. "Spectrum and Energy of the Sombor Matrix." Vojnoteh. Glas. 69, 551-561, 2021.Liu, H.; You, L.; Huang, Y.; Fang, S. "Spectral Properties of
-Sombor
Matrices and Beyond." MATCH Commun. Math. Comput. Chem. 87, 59-87,
2022.Zheng, L.; Tian, G.; and Cui, S. "On Spectral Radius and Energy
of Arithmetic-Geometric Matrix of Graphs." MATCH Commun. Math. Comput. Chem. 83,
635-650, 2020.Zheng, R.; Su, P.; and Jin. S. "Arithmetic-Geometric
Matrix of Graphs and Its Applications." Appl. Math. Comput. 42,
127764, 1-11, 2023.
Cite this as:
Weisstein, Eric W. "Sombor Spectral Radius." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SomborSpectralRadius.html