Semiregular automorphisms of vertex-transitive graphs of certain valencies

• Autores: Edward Dobson, Aleksander Malnic , Dragan Maru¿ic, Lewis A. Nowitz
• Localización: Journal of combinatorial theory. Series B, ISSN 0095-8956, Vol. 97, Nº. 3, 2007, págs. 371-380
• Idioma: inglés
• DOI: 10.1016/j.jctb.2006.06.004
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• Resumen

  • It is shown that a vertex-transitive graph of valency p+1, p a prime, admitting a transitive action of a {2,p}-group, has a non-identity semiregular automorphism. As a consequence, it is proved that a quartic vertex-transitive graph has a non-identity semiregular automorphism, thus giving a partial affirmative answer to the conjecture that all vertex-transitive graphs have such an automorphism and, more generally, that all 2-closed transitive permutation groups contain such an element (see [D. Maru¿ic, On vertex symmetric digraphs, Discrete Math. 36 (1981) 69¿81; P.J. Cameron (Ed.), Problems from the Fifteenth British Combinatorial Conference, Discrete Math. 167/168 (1997) 605¿615]).