Commuting graphs and extremal centralizers

Gregor Dolinar, Alexander Guterman, Bojan Kuzma, Polona Oblak

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We determine the conditions for matrix centralizers which can guarantee the connectedness of the commuting graph for the full matrix algebra M n(F) over an arbitrary field F. It is known that if F is an algebraically closed field and n ≥ 3, then the diameter of the commuting graph of Mn(F) is always equal to four. We construct a concrete example showing that if F is not algebraically closed, then the commuting graph of Mn(F) can be connected with the diameter at least five.

Original languageEnglish
Pages (from-to)453-459
Number of pages7
JournalArs Mathematica Contemporanea
Volume7
Issue number2
DOIs
StatePublished - 2014
Externally publishedYes

Keywords

  • Centralizer
  • Commuting graph
  • Matrix ring

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