On Vertex-transitive Cayley Graphs of Finite Transformation Semigroups with Restricted Range

Authors

  • Chunya Tisklang Thai Government Scholarships in the Area of Science and Technology (Ministry of Science and Technology) 111 Thailang Science Park, Patumthani 12120, Thailand; Department of Mathematics Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
  • Sayan Panma Department of Mathematics Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand Centre of Excellence in Mathematics, CHE, Bangkok 10400, Thailand

DOI:

https://doi.org/10.26713/cma.v9i2.640

Keywords:

Cayley graph, Vertex-transitive graph, Transformation semigroup, Restricted range

Abstract

Let \(T(X)\) be the semigroup of all transformations on a set \(X\). For a non-empty subset \(Y\) of \(X\), denoted by \(T(X,Y)\) the subsemigroup of \(T(X)\) consisting of all transformations whose range is contained in \(Y\).  Kelarev and  Praeger in [9] gave necessary and sufficient conditions for all vertex-transitive Cayley graphs of semigroups. In this paper, we give similar descriptions for all vertex-transitive Cayley graphs of \(T(X,Y)\).

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Published

30-06-2018
CITATION

How to Cite

Tisklang, C., & Panma, S. (2018). On Vertex-transitive Cayley Graphs of Finite Transformation Semigroups with Restricted Range. Communications in Mathematics and Applications, 9(2), 219–227. https://doi.org/10.26713/cma.v9i2.640

Issue

Vol. 9 No. 2 (2018)

Section

Research Article

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