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arXiv · 1009.5543

On maximal distances in a commuting graph

Gregor Dolinar·Bojan Kuzma·Polona Oblak
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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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Gregor Dolinar, Bojan Kuzma, Polona Oblak. 2010-09-28. On maximal distances in a commuting graph. https://arxiv.org/abs/1009.5543

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