Power graphs of full transformation semigroups

LingLi Zeng, YanLiang Cheng, BoXing Yang, Yong Shao

Abstract


In this paper we characterize completely the connected components of the power graph of the full transformation semigroup T_X on a finite set X and provide the necessary and sufficient conditions for which the connected component is a semigroup.
We also demonstrate that the power graph of T_X is planar if and only if |X| \leq 4.


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