On the diameter of the commuting graph of the full matrix ring over the real numbers

Document Type : Research Paper


1 Departamento de Matemáticas‎, ‎Universidad de Oviedo‎. ‎Avenida Calvo Sotelo s/n‎, ‎33007 Oviedo‎, ‎Spain.

2 Centro Universitario de la Defensa de Zaragoza‎. ‎Carretera de Huesca s/n‎, ‎50090 Zaragoza‎, ‎Spain.


‎In a recent paper C‎. ‎Miguel proved that the diameter of the commuting graph of the matrix ring $\mathrm{M}_n(\mathbb{R})$ is equal to $4$ if either $n=3$ or $n\geq5$‎. ‎But the case $n=4$ remained open‎, ‎since the diameter could be $4$ or $5$‎. ‎In this work we close the problem showing that also in this case the diameter is $4$.


Main Subjects

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Volume 43, Issue 1
February 2017
Pages 217-221
  • Receive Date: 09 June 2014
  • Revise Date: 03 November 2015
  • Accept Date: 14 February 2017
  • First Publish Date: 22 February 2017