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 1 - 10 / 22123 1.Automorphism groups of wreath product digraphsEdward Dobson, Joy Morris, 2009, original scientific articleFound in: osebiKeywords: wreath product digraph, automorphism groupPublished: 15.10.2013; Views: 2073; Downloads: 6 Full text (0,00 KB)This document has more files! More... 2.An unusual decomposition of a complete 7-partite graph of order 28Edward Dobson, Dragan Marušič, 2008, original scientific articleAbstract: A decomposition of the complete 7-partite graph on 28 vertices where each set in the partition has four vertices is given. Several unusual properties of this decomposition are discussed, giving rise to several natural questions.Found in: osebiKeywords: matematika, teorija grafov, po točkah tranzitivni grafi, faktorizacijaPublished: 15.10.2013; Views: 1691; Downloads: 43 Full text (0,00 KB) 3.Some non-normal Cayley digraphs of the generalized quaternion group of certain ordersEdward Dobson, 2003, original scientific articleFound in: osebiKeywords: non-normal Cayley digraph, generalized quaternion groupPublished: 15.10.2013; Views: 1833; Downloads: 8 Full text (0,00 KB)This document has more files! More... 4.The full automorphism group of Cayley graphs of ${mathbb Z}_ptimes{mathbbZ}_{p^2}$Edward Dobson, 2012, original scientific articleFound in: osebiKeywords: Cayley graph, abelian group, automorphism groupPublished: 15.10.2013; Views: 1717; Downloads: 31 Full text (0,00 KB) 5.On the proof of a theorem of PálfyEdward Dobson, 2006, original scientific articleFound in: osebiKeywords: CI-group, Euler's phi functionPublished: 15.10.2013; Views: 1602; Downloads: 10 Full text (0,00 KB)This document has more files! More... 6.Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power orderEdward Dobson, 2010, original scientific articleAbstract: We show that almost every Cayley graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order has automorphism group as small as possible. Additionally, we show that almost every Cayley (di)graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order that does not have automorphism group as small as possible is a normal Cayley (di)graph of ▫$G$▫ (that is, ▫$G_L \triangleleft {\rm Aut}(\Gamma))$▫.Found in: osebiKeywords: mathematics, graph theory, Cayley graph, abelian group, automorphism group, asymptotic, ▫$p$▫-groupPublished: 15.10.2013; Views: 2401; Downloads: 51 Full text (0,00 KB) 7.Automorphism groups of Cayley digraphs of Zp3Edward Dobson, István Kovács, 2009, original scientific articleFound in: osebiKeywords: Cayley digraph, automorphism groupPublished: 15.10.2013; Views: 2202; Downloads: 8 Full text (0,00 KB)This document has more files! More... 8.On overgroups of regular abelian p-groupsEdward Dobson, 2009, original scientific articleAbstract: Let ▫$G$▫ be a transitive group of odd prime-power degree whose Sylow ▫$p$▫-subgroup ▫$P$▫ is abelian od rank ▫$t$▫. Weshow that if ▫$p > 2^{t-1}$▫, then ▫$G$▫ has a normal subgroup that is a direct product of ▫$t$▫ permutation groups of smaller degree that are either cyclic or doubly-transitive simple groups. As a consequence, we determine the full automorphism group of a Cayley diagraph of an abelian group with rank two such that the Sylow ▫$p$▫-subgroup of the full automorphism group is abelian.Found in: osebiKeywords: group theory, graph theory, Cayley graph, abelian group, regular group, p-groupPublished: 15.10.2013; Views: 1522; Downloads: 54 Full text (0,00 KB) 9.Minimal normal subgroups of transitive permutation groups of square-free degreeAleksander Malnič, Dragan Marušič, Edward Dobson, Lewis A. Nowitz, 2007, original scientific articleAbstract: It is shown that a minimal normal subgroup of a transitive permutation group of square-free degree in its induced action is simple and quasiprimitive, with three exceptions related to ▫$A_5$▫, ▫$A_7$▫, and PSL(2,29). Moreover, it is shown that a minimal normal subgroup of a 2-closed permutation group of square-free degree in its induced action is simple. As an almost immediate consequence, it follows that a 2-closed transitive permutation group of square-free degree contains a semiregular element of prime order, thus giving a partial affirmative answer to the conjecture 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]).Found in: osebiKeywords: mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graphPublished: 03.04.2017; Views: 836; Downloads: 43 Full text (0,00 KB) 10.Semiregular automorphisms of vertex-transitive graphs of certain valenciesDragan Marušič, Edward Dobson, Aleksander Malnič, Lewis A. Nowitz, 2007, original scientific articleAbstract: 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]).Found in: osebiKeywords: mathematics, graph theory, transitive permutation group, 2-closed group, semiregular automorphism, vertex-transitive graphPublished: 03.04.2017; Views: 800; Downloads: 39 Full text (0,00 KB)
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