20.500.12556/RUP-7722 Semiregular automorphisms of vertex-transitive graphs of certain valencies 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 matematika teorija grafov tranzitivna permutacijska grupa 2-zaprta grupa polregularni avtomorfizem točkovno tranzitivni grafi true true false Angleški jezik Angleški jezik Delo ni kategorizirano 2016-04-08 16:46:27 2017-04-03 08:13:28 2024-03-01 13:33:23 0000-00-00 00:00:00 2007 0 0 str. 371-380 iss. 3 Vol. 97 2007 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0095-8956 519.17:512.54 25721600 14287961 http://dx.doi.org/10.1016/j.jctb.2006.06.004 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=7722 Inštitut Andrej Marušič 0 0 0