Multiples of left loops and vertex-transitive graphs

Eric Mwambene

Open Mathematics (2005)

  • Volume: 3, Issue: 2, page 245-250
  • ISSN: 2391-5455

Abstract

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Via representation of vertex-transitive graphs on groupoids, we show that left loops with units are factors of groups, i.e., left loops are transversals of left cosets on which it is possible to define a binary operation which allows left cancellation.

How to cite

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Eric Mwambene. "Multiples of left loops and vertex-transitive graphs." Open Mathematics 3.2 (2005): 245-250. <http://eudml.org/doc/268890>.

@article{EricMwambene2005,
abstract = {Via representation of vertex-transitive graphs on groupoids, we show that left loops with units are factors of groups, i.e., left loops are transversals of left cosets on which it is possible to define a binary operation which allows left cancellation.},
author = {Eric Mwambene},
journal = {Open Mathematics},
keywords = {05C25; 20B25},
language = {eng},
number = {2},
pages = {245-250},
title = {Multiples of left loops and vertex-transitive graphs},
url = {http://eudml.org/doc/268890},
volume = {3},
year = {2005},
}

TY - JOUR
AU - Eric Mwambene
TI - Multiples of left loops and vertex-transitive graphs
JO - Open Mathematics
PY - 2005
VL - 3
IS - 2
SP - 245
EP - 250
AB - Via representation of vertex-transitive graphs on groupoids, we show that left loops with units are factors of groups, i.e., left loops are transversals of left cosets on which it is possible to define a binary operation which allows left cancellation.
LA - eng
KW - 05C25; 20B25
UR - http://eudml.org/doc/268890
ER -

References

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  1. [1] A.A. Albert: “Quasigroups I”, Trans. Amer. Math. Soc., Vol. 54, (1943), pp. 507–520. http://dx.doi.org/10.2307/1990259 
  2. [2] W. Dörfler: “Every regular graph is a quasi-regular graph”, Discrete Math., Vol. 10, (1974), pp. 181–183. http://dx.doi.org/10.1016/0012-365X(74)90031-4 
  3. [3] E. Mwambene: Representing graphs on Groupoids: symmetry and form, Thesis (PhD), University of Vienna, 2001. 
  4. [4] G. Gauyacq: “On quasi-Cayley graphs”, Discrete Appl. Math., Vol. 77, (1997), pp. 43–58. http://dx.doi.org/10.1016/S0166-218X(97)00098-X Zbl0881.05057
  5. [5] C. Praeger: “Finite Transitive permutation groups and finite vertex-transitive graphs”, In: G. Sabidussi and G. Hahn (Eds.): Graph Symmetry: Algebraic Methods and Applications, NATO ASI Series, Vol. 497, Kluwer Academic Publishers, The Netherlands, Dordrecht, 1997. Zbl0885.05072
  6. [6] G. Sabidussi: “Vertex-transitive graphs”, Monatsh. Math., Vol. 68, (1964), pp. 426–438. http://dx.doi.org/10.1007/BF01304186 Zbl0136.44608

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