The Sombor matrix 
of a simple graph is a weighted adjacency
matrix with weight
 |
(1) |
where 
are the vertex degrees of the graph. In other words,
![[A_(Sombor)]_(ij)={sqrt(d_i^2+d_j^2) for i,j adjacent; 0 otherwise](https://txtdot.deep-swarm.xyz/proxy/img?url=https%3A%2F%2Fmathworld.wolfram.com%2Fimages%2Fequations%2FSomborMatrix%2FNumberedEquation2.svg) |
(2) |
(Zheng et al. 2022).
Its largest eigenvalue is called the Sombor spectral radius, half the sum of its matrix elements is the Sombor index, and the sum of absolute values of its eigenvalues is the Sombor energy.
See also
Sombor Energy, Sombor Index, Sombor Spectral Radius, Adjacency Matrix, Weighted Adjacency Matrix
Explore 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.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Sombor Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SomborMatrix.html