English

A matrix ring with commuting graph of maximal diameter

Combinatorics 2016-03-11 v2

Abstract

The commuting graph of a semigroup is the set of non-central elements; the edges are defined as pairs (u,v)(u,v) satisfying uv=vuuv=vu. We provide an example of a field FF and an integer nn such that the commuting graph of Matn(F)\operatorname{Mat}_n(F) has maximal possible diameter, equal to six.

Keywords

Cite

@article{arxiv.1501.02764,
  title  = {A matrix ring with commuting graph of maximal diameter},
  author = {Yaroslav Shitov},
  journal= {arXiv preprint arXiv:1501.02764},
  year   = {2016}
}

Comments

7 pages; a corrected version which is to appear in JCTA. The description of the field was incorrect in the first version

R2 v1 2026-06-22T07:58:48.590Z