Commuting graphs of full matrix rings over finite fields.

DOI10.1016/j.laa.2008.01.036zbMath1155.16022OpenAlexW1989280699MaRDI QIDQ924367

Alireza Abdollahi

Publication date: 15 May 2008

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.01.036

zbMATH Keywords

matrix ringscommuting graphs of rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Finite rings and finite-dimensional associative algebras (16P10) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Center, normalizer (invariant elements) (associative rings and algebras) (16U70)

Related Items (25)

Perfect codes and universal adjacency spectra of commuting graphs of finite groups ⋮ Non-commuting graphs of rings ⋮ Automorphism group of the commuting graph of \(2\times 2\) matrix ring over \(\mathbb{Z}_{p^s}\) ⋮ Unnamed Item ⋮ On Distance Laplacian (Signless) Eigenvalues of Commuting Graphs of Dihedral and Dicyclic Groups ⋮ Automorphisms of a commuting graph of rank one upper triangular matrices ⋮ The automorphism group and fixing number of the orthogonality graph of the full matrix ring ⋮ The commuting graph of the ring M ₃ (F _q ) ⋮ Graphs defined by orthogonality. ⋮ Diameters of commuting graphs of matrices over semirings ⋮ Unnamed Item ⋮ Commuting involution graphs for 4-dimensional projective symplectic groups ⋮ Commuting graphs of generalized dihedral groups ⋮ On a conjecture about the commuting graphs of finite matrix rings ⋮ On Commuting Graphs of Finite Matrix Rings ⋮ On diameter of components in commuting graphs ⋮ Various spectra and energies of commuting graphs of finite rings ⋮ Automorphism group of an ideal-relation graph over a matrix ring ⋮ Spectrum and genus of commuting graphs of some classes of finite rings ⋮ On the Commuting Graph of Dihedral Group ⋮ Unnamed Item ⋮ Unnamed Item ⋮ DIAMETER OF COMMUTING GRAPHS OF SYMPLECTIC ALGEBRAS ⋮ A generalization of commuting graphs ⋮ The connectivity and the spectral radius of commuting graphs on certain finite groups

Uses Software

• GAP

Cites Work

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• On the diameters of commuting graphs
• On commuting graphs of semisimple rings
• Non-commuting graph of a group.
• Equally partitioned groups
• Exceptional solutions of the exponential diophantine equation (x3 - 1) / (x - 1) = (yn - 1) / (y - 1)

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