On maximal distances in a commuting graph

2010/09/28 by Gregor Dolinar, Dolinar, Gregor, Bojan Kuzma +3
Mathematics · #05C12 #05C50 #15A27 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:05C12 #msc:05C50 #msc:15A27

paper · pdf · doi:10.48550/arxiv.1009.5543

arxiv created 2010/09/28 · arxiv updated 2010/09/29

Abstract

We study maximal distances in the commuting graphs of matrix algebras defined over algebraically closed fields. In particular, we show that the maximal distance can be attained only between two nonderogatory matrices. We also describe rank-one and semisimple matrices using the distances in the commuting graph.

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