Cayley Graphs of Transformation Semigroups with Restriction on the Fixed Set is Bijective

Authors

  • Ekkachai Laysirikul
  • Natthawarun Pinin
  • Yanisa Chaiya

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i2.7605

Keywords:

transformation semigroup, Cayley graph, connectedness, domination parameters

Abstract

Let $PG_Y(X)=\{\alpha \in T(X) : \alpha|_Y \in G(Y)\}$ be a subsemigroup of the full transformation semigroup $T(X)$, where the restriction of each transformation to $Y$ is a permutation of $Y$. 
This structure can be viewed as an extension of the symmetric group to a transformation semigroup.
In this paper, we study the Cayley digraphs $\operatorname{Cay}(PG_Y(X),A)$ generated by a nonempty set $A$ of minimal idempotents. We describe basic structural properties of these digraphs, including initial and terminal vertices. We also examine their degrees, connectedness, and completeness. In addition, domination parameters of these digraphs are determined.

References

Downloads

Published

2026-07-28

Issue

Vol. 19 No. 2: (April 2026)

Section

Algebra

License

Copyright (c) 2026 Ekkachai Laysirikul, Natthawarun Pinin, Yanisa Chaiya

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Cayley Graphs of Transformation Semigroups with Restriction on the Fixed Set is Bijective. (2026). European Journal of Pure and Applied Mathematics, 19(2), 7605. https://doi.org/10.29020/nybg.ejpam.v19i2.7605