Cayley color graphs of inverse semigroups and groupoids

Nándor Sieben

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 3, page 683-692
  • ISSN: 0011-4642

Abstract

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The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.

How to cite

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Sieben, Nándor. "Cayley color graphs of inverse semigroups and groupoids." Czechoslovak Mathematical Journal 58.3 (2008): 683-692. <http://eudml.org/doc/37860>.

@article{Sieben2008,
abstract = {The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.},
author = {Sieben, Nándor},
journal = {Czechoslovak Mathematical Journal},
keywords = {Cayley color graph; inverse semigroup; groupoid; Cayley color graphs; inverse semigroups; inverse groupoids; partial automorphisms},
language = {eng},
number = {3},
pages = {683-692},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Cayley color graphs of inverse semigroups and groupoids},
url = {http://eudml.org/doc/37860},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Sieben, Nándor
TI - Cayley color graphs of inverse semigroups and groupoids
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 3
SP - 683
EP - 692
AB - The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.
LA - eng
KW - Cayley color graph; inverse semigroup; groupoid; Cayley color graphs; inverse semigroups; inverse groupoids; partial automorphisms
UR - http://eudml.org/doc/37860
ER -

References

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  1. Brown, R., 10.1112/blms/19.2.113, Bull. London Math. Soc. 19 (1987), 113-134. (1987) Zbl0612.20032MR0872125DOI10.1112/blms/19.2.113
  2. Fiol, M. L., Fiol, M. A., Yebra, J. L. A., When the arc-colored line digraph of a Cayley colored digraph is again a Cayley colored digraph, Ars Combinatoria 34 (1992), 65-73. (1992) Zbl0773.05048MR1206550
  3. Gross, J. L., Tucker, T. W., Topological graph theory, Wiley Interscience Series in Discrete Mathematics and Optimization (1987). (1987) Zbl0621.05013MR0898434
  4. Muhly, P. S., CBMS Lecture Notes, Texas Christian University, May (1990). (1990) 
  5. Petrich, M., Inverse semigroups, John Wiley & Sons, New York (1984). (1984) Zbl0546.20053MR0752899
  6. Renault, J. N., A groupoid approach to C * -algebras, Lecture Notes in Mathematics, Vol 793, Springer-Verlag, New York (1980). (1980) Zbl0433.46049MR0584266
  7. White, A. T., Graphs, Groups and Surfaces, North-Holland, Amsterdam (1973). (1973) Zbl0268.05102

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