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arXiv · 1710.05250

Commuting Graphs of Boundedly Generated Semigroups

Tomer Bauer·Be'eri Greenfeld
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Abstract

Ara\'ujo, Kinyon and Konieczny (2011) pose several problems concerning the construction of arbitrary commuting graphs of semigroups. We observe that every star-free graph is the commuting graph of some semigroup. Consequently, we suggest modifications for some of the original problems, generalized to the context of families of semigroups with a bounded number of generators, and pose related problems. We construct monomial semigroups with a bounded number of generators, whose commuting graphs have an arbitrary clique number. In contrast to that, we show that the diameter of the commuting graphs of semigroups in a wider class (containing the class of nilpotent semigroups), is bounded by the minimal number of generators plus two. We also address a problem concerning knit degree.

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Tomer Bauer, Be'eri Greenfeld. 2017-10-14. Commuting Graphs of Boundedly Generated Semigroups. https://doi.org/10.1016/j.ejc.2016.02.009

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