On Connectedness of Cayley Graphs of Finite Transformation Semigroups

Chunya Tisklang, Sayan Panma

Abstract


For a fixed non-empty subset $Y$ of $X$, we denote by $T(X,Y)$ the semigroup consisting of all transformations on $X$ whose range is contained in $Y$.  In this paper, we investigate connectedness of Cayley graphs of finite transformation semigroups with restricted range.  Necessary and sufficient conditions for Cayley graph of $\txy$ to be strongly connected, unilaterally connected, and weakly connected are given.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|