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1.
Automorphism groups of wreath product digraphs
Edward Dobson, Joy Morris, 2009, original scientific article

Found in: osebi
Keywords: wreath product digraph, automorphism group
Published: 15.10.2013; Views: 2070; Downloads: 6
URL Full text (0,00 KB)
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2.
An unusual decomposition of a complete 7-partite graph of order 28
Edward Dobson, Dragan Marušič, 2008, original scientific article

Abstract: 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: osebi
Keywords: matematika, teorija grafov, po točkah tranzitivni grafi, faktorizacija
Published: 15.10.2013; Views: 1690; Downloads: 43
URL Full text (0,00 KB)

3.
Some non-normal Cayley digraphs of the generalized quaternion group of certain orders
Edward Dobson, 2003, original scientific article

Found in: osebi
Keywords: non-normal Cayley digraph, generalized quaternion group
Published: 15.10.2013; Views: 1829; Downloads: 8
URL Full text (0,00 KB)
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4.
The full automorphism group of Cayley graphs of ${mathbb Z}_ptimes{mathbbZ}_{p^2}$
Edward Dobson, 2012, original scientific article

Found in: osebi
Keywords: Cayley graph, abelian group, automorphism group
Published: 15.10.2013; Views: 1713; Downloads: 31
URL Full text (0,00 KB)

5.
On the proof of a theorem of Pálfy
Edward Dobson, 2006, original scientific article

Found in: osebi
Keywords: CI-group, Euler's phi function
Published: 15.10.2013; Views: 1600; Downloads: 10
URL Full text (0,00 KB)
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6.
Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order
Edward Dobson, 2010, original scientific article

Abstract: 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: osebi
Keywords: mathematics, graph theory, Cayley graph, abelian group, automorphism group, asymptotic, ▫$p$▫-group
Published: 15.10.2013; Views: 2396; Downloads: 51
URL Full text (0,00 KB)

7.
Automorphism groups of Cayley digraphs of Zp3
Edward Dobson, István Kovács, 2009, original scientific article

Found in: osebi
Keywords: Cayley digraph, automorphism group
Published: 15.10.2013; Views: 2201; Downloads: 8
URL Full text (0,00 KB)
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8.
On overgroups of regular abelian p-groups
Edward Dobson, 2009, original scientific article

Abstract: 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: osebi
Keywords: group theory, graph theory, Cayley graph, abelian group, regular group, p-group
Published: 15.10.2013; Views: 1518; Downloads: 54
URL Full text (0,00 KB)

9.
Minimal normal subgroups of transitive permutation groups of square-free degree
Aleksander Malnič, Dragan Marušič, Edward Dobson, Lewis A. Nowitz, 2007, original scientific article

Abstract: 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: osebi
Keywords: mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graph
Published: 03.04.2017; Views: 834; Downloads: 43
URL Full text (0,00 KB)

10.
Semiregular automorphisms of vertex-transitive graphs of certain valencies
Dragan Marušič, Edward Dobson, Aleksander Malnič, Lewis A. Nowitz, 2007, original scientific article

Abstract: 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: osebi
Keywords: mathematics, graph theory, transitive permutation group, 2-closed group, semiregular automorphism, vertex-transitive graph
Published: 03.04.2017; Views: 798; Downloads: 39
URL Full text (0,00 KB)

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