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- W4298294419 abstract "Given any digraph $D$ without loops or multiple arcs, there is a natural construction of a semigroup $langle Drangle$ of transformations. To every arc $(a,b)$ of $D$ is associated the idempotent transformation $(ato b)$ mapping $a$ to $b$ and fixing all vertices other than $a$. The semigroup $langle Drangle$ is generated by the idempotent transformations $(ato b)$ for all arcs $(a,b)$ of $D$. In this paper, we consider the question of when there is a transformation in $langle Drangle$ containing a large cycle, and, for fixed $kin mathbb N$, we give a linear time algorithm to verify if $langle Drangle$ contains a transformation with a cycle of length $k$. We also classify those digraphs $D$ such that $langle Drangle$ has one of the following properties: inverse, completely regular, commutative, simple, 0-simple, a semilattice, a rectangular band, congruence-free, is $mathscr{K}$-trivial or $mathscr{K}$-universal where $mathscr{K}$ is any of Green's $mathscr{H}$-, $mathscr{L}$-, $mathscr{R}$-, or $mathscr{J}$-relation, and when $langle Drangle$ has a left, right, or two-sided zero." @default.
- W4298294419 created "2022-10-01" @default.
- W4298294419 creator A5037486046 @default.
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- W4298294419 date "2017-04-04" @default.
- W4298294419 modified "2023-10-05" @default.
- W4298294419 title "Structural aspects of semigroups based on digraphs" @default.
- W4298294419 doi "https://doi.org/10.48550/arxiv.1704.00937" @default.
- W4298294419 hasPublicationYear "2017" @default.
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