We consider 2-factorizations of complete graphs which possess an automorphism group fixing k\ge 0 vertices and acting sharply transitively on the others. We study the structures of such factorizations and consider the cases in which the group is either abelian or dihedral in somemore details. We prove that the class of 2-factorizations of complete graphs is universal. Namely each finite group is the full automorphism group of a 2-factorization of the class.
On 2-factorizations of the complete graph: from the k-pyramidal to the universal property / Bonvicini, Simona; G., Mazzuoccolo; Rinaldi, Gloria. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - STAMPA. - 17:3(2009), pp. 211-228. [10.1002/jcd.20205]
On 2-factorizations of the complete graph: from the k-pyramidal to the universal property
BONVICINI, Simona;G. Mazzuoccolo;RINALDI, Gloria
2009
Abstract
We consider 2-factorizations of complete graphs which possess an automorphism group fixing k\ge 0 vertices and acting sharply transitively on the others. We study the structures of such factorizations and consider the cases in which the group is either abelian or dihedral in somemore details. We prove that the class of 2-factorizations of complete graphs is universal. Namely each finite group is the full automorphism group of a 2-factorization of the class.
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k_pyrUniversa_rivista2009.pdf
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