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Title: Semiregular automorphisms of vertex-transitive graphs of certain valencies Marušič, Dragan (Author)Dobson, Edward (Author)Malnič, Aleksander (Author)Nowitz, Lewis A. (Author) http://dx.doi.org/10.1016/j.jctb.2006.06.004 English Not categorized 1.01 - Original Scientific Article IAM - Andrej Marušič Institute 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. 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]). mathematics, graph theory, transitive permutation group, 2-closed group, semiregular automorphism, vertex-transitive graph 2007 str. 371-380 Vol. 97, iss. 3 0095-8956 519.17:512.54 14287961 1056 51 Document is not linked to any category.

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## Secondary language

Language: English matematika, teorija grafov, tranzitivna permutacijska grupa, 2-zaprta grupa, polregularni avtomorfizem, točkovno tranzitivni grafi