Multiples of left loops and vertex-transitive graphs

• Autorzy: Eric Mwambene
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Vertex-transitive graphs; groupoids, loops; 05C25; 20B25

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2005
• Tom: 3
• Numer: 2
• Strony: 245-250

Daty

wydano

2005-06-01

online

2005-06-01

Twórcy

autor

Eric Mwambene

• University of the Western Cape

Bibliografia

• [1] A.A. Albert: “Quasigroups I”, Trans. Amer. Math. Soc., Vol. 54, (1943), pp. 507–520. http://dx.doi.org/10.2307/1990259
• [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] E. Mwambene: Representing graphs on Groupoids: symmetry and form, Thesis (PhD), University of Vienna, 2001.
• [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
• [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.
• [6] G. Sabidussi: “Vertex-transitive graphs”, Monatsh. Math., Vol. 68, (1964), pp. 426–438. http://dx.doi.org/10.1007/BF01304186

Identyfikatory

DOI

10.2478/BF02479200