A matrix ring with commuting graph of maximal diameter

Abstract

The commuting graph of a semigroup is the set of non-central elements; the edges are defined as pairs $(u,v)$ satisfying $uv=vu$. We provide an example of a field $F$ and an integer $n$ such that the commuting graph of ${\mathrm{Mat}}_n(F)$ has maximal possible diameter, equal to six.

7 pages; a corrected version which is to appear in JCTA. The description of the field was incorrect in the first version

References in corpus (4)

• Diameters of commuting graphs of matrices over semirings
• Minimal paths in the commuting graphs of semigroups
• A note on commuting graphs of matrix rings over fields
• Diameter of the commuting graph of ${\mathbb{R}}^{n\times n}$

Cited by in corpus (5)

• A note on commuting graphs of matrix rings over fields
• Commuting involution graphs of linear groups
• The cyclic graph of a semigroup
• Commuting graphs of Okubo algebras
• Compressed commuting graphs of matrix rings