Identifies maximal subsemigroups in endomorphism monoids of star graphs, indicating their structural properties.
In this paper, we determine the maximal subsemigroups of the singular part of endomorphism monoids of the star graphs Sn, for a given positive integer n, namely End(Sn), wEnd(Sn), and swEnd(Sn), respectively. The monoid wEnd(Sn) of all weak endomorphisms on Sn, the monoid End(Sn) of all endomorphisms on Sn as well as the monoid swEnd(Sn) of all strong weak endomorphisms on Sn is regular. We also determine the maximal regular submonoids of the singular part of wEnd(Sn), End(Sn), and swEnd(Sn).
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Koppitz et al. (2025) studied this question.
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