Semiregular automorphisms of vertex-transitive graphs of certain valenciesDobson, Edward Tauscher (Avtor) Malnič, Aleksander (Avtor) Marušič, Dragan (Avtor) Nowitz, Lewis A. (Avtor) mathematicsgraph theorytransitive permutation group2-closed groupsemiregular automorphismvertex-transitive graphIt 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. Marušic, 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]).20072016-04-08 16:46:27Delo ni kategorizirano7722sl