Commuting graphs and extremal centralizers

Gregor Dolinar; Alexander Guterman; Bojan Kuzma; Polona Oblak

doi:10.26493/1855-3974.386.a83

Commuting graphs and extremal centralizers

Gregor Dolinar, Alexander Guterman, Bojan Kuzma, Polona Oblak

Research output: Contribution to journal › Article › peer-review

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 M_n(F) is always equal to four. We construct a concrete example showing that if F is not algebraically closed, then the commuting graph of M_n(F) can be connected with the diameter at least five.

Original language	English
Pages (from-to)	453-459
Number of pages	7
Journal	Ars Mathematica Contemporanea
Volume	7
Issue number	2
DOIs	https://doi.org/10.26493/1855-3974.386.a83
State	Published - 2014
Externally published	Yes

Keywords

Centralizer
Commuting graph
Matrix ring

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Algebra and Number Theory
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.26493/1855-3974.386.a83

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AU - Dolinar, Gregor

AU - Guterman, Alexander

AU - Kuzma, Bojan

AU - Oblak, Polona

PY - 2014

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N2 - 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.

AB - 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.

KW - Centralizer

KW - Commuting graph

KW - Matrix ring

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DO - 10.26493/1855-3974.386.a83

M3 - مقالة

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EP - 459

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

IS - 2

ER -

Commuting graphs and extremal centralizers

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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