Commuting graphs of boundedly generated semigroups. (August 2016)

• Record Type: Journal Article
• Authors: Bauer, Tomer; Greenfeld, Be'eri
• Is Part Of: European journal of combinatorics. Volume 56(2016:Aug.)
• Page Start: 40
• Page End: 45
• Publication Date: 2016-08
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2016.02.009
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: Araújo, 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.