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arXiv · 2511.10221

Diameters of commuting graphs of partial transformation semigroups

Tânia Paulista
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Abstract

Let $X$ be a finite set. We determine the diameter of the commuting graph of the partial transformation semigroup $\mathcal{P}(X)$ on $X$ and show that it coincides with the diameter of the commuting graph of the transformation semigroup $\mathcal{T}(X)$ 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.

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Tânia Paulista. 2025-11-13. Diameters of commuting graphs of partial transformation semigroups. https://arxiv.org/abs/2511.10221

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