Diameters of commuting graphs of partial transformation semigroups

2025/11/13 by Tânia Paulista, Paulista, Tânia
Computer Science · Mathematics · #05C12 #05C25 #20M20 #Advanced Operator Algebra Research #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Limits and Structures in Graph Theory #Rings and Algebras (math.RA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2511.10221

openalex publication_date 2025/11/13 · openalex created_date 2025/11/15 · openalex updated_date 2026/07/28

Abstract

Let X be a finite set. We determine the diameter of the commuting graph of the partial transformation semigroup P(X) on X and show that it coincides with the diameter of the commuting graph of the transformation semigroup T(X) on X, which was previously determined by Araújo, Kinyon and Konieczny. This proves the existence of a semigroup S and of a proper subsemigroups T of S such that the diameters of the commuting graphs of S and T are equal.

Related

• Characterizing the largest commutative (full and partial) transformation semigroups of certain types
• Commuting graphs of completely simple semigroups
• On Bounding the Diameter of the Commuting Graph of a Group
• The Commuting Graph of the Symmetric Inverse Semigroup
• There is no upper bound for the diameter of the commuting graph of a finite group