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Sombor Matrix

The Sombor matrix A_(Sombor) of a simple graph is a weighted adjacency matrix with weight

f(d_i,d_j)=sqrt(d_i^2+d_j^2),
(1)

where d_i 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
(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

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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 p-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. bf 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 Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SomborMatrix.html

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