0 KB335 KB43 KB200820252010Feng, Yan-QuanWang, Xiuyunštevilka:2letnik:3str. 151-163COBISSID:15859033ISSN:1855-3966URN:URN:NBN:SI:doc-HLAR8KK0enDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneaCayleyjevi grafimatematikateorija grafovtranzitivni grafiHalf-arc-transitive graphs of order 4p of valency twice a prime|A graph is half-arc-transitive if its automorphism group acts transitively on vertices and edges, but not on arcs. Let ?$p$? be a prime. Cheng and Oxley On weakly symmetric graphs of order twice a prime, J. Combin. Theory B 42 (1987),196-211 proved that there is no half-arc-transitive graph of order ?$2p$?, and Alspach and Xu 1/2-transitive graphs of order ?$3p$?, J. Algebraic Combin. 3 (1994), 347-355 classified half-arc-transitive graphs of order ?$3p$?. In this paper we classify half-arc-transitive graphs of order ?$4p$? of valency ?$2q$? for each prime ?$q \ge 5$?. It is shown that such graphs exist if and only if ?$p - 1$? is divisible by ?$4q$?. Moreover, for such ?$p$? and ?$q$? a unique half-arc-transitive graph of order ?$4p$? and valency ?$2q$? exists and this graph is a Cayley graphTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije