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1.
Automorphism groups of wreath product digraphs
Edward Dobson, Joy Morris, 2009, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: wreath product digraph, automorphism group
Objavljeno: 15.10.2013; Ogledov: 2006; Prenosov: 6
URL Polno besedilo (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, izvirni znanstveni članek

Opis: 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.
Najdeno v: osebi
Ključne besede: matematika, teorija grafov, po točkah tranzitivni grafi, faktorizacija
Objavljeno: 15.10.2013; Ogledov: 1612; Prenosov: 19
URL Polno besedilo (0,00 KB)

3.
Some non-normal Cayley digraphs of the generalized quaternion group of certain orders
Edward Dobson, 2003, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: non-normal Cayley digraph, generalized quaternion group
Objavljeno: 15.10.2013; Ogledov: 1776; Prenosov: 8
URL Polno besedilo (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, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: Cayley graph, abelian group, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1657; Prenosov: 29
URL Polno besedilo (0,00 KB)

5.
On the proof of a theorem of Pálfy
Edward Dobson, 2006, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: CI-group, Euler's phi function
Objavljeno: 15.10.2013; Ogledov: 1543; Prenosov: 10
URL Polno besedilo (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, izvirni znanstveni članek

Opis: 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, ▫$G_L \triangleleft {\rm Aut}(\Gamma))$▫.
Najdeno v: osebi
Ključne besede: mathematics, graph theory, Cayley graph, abelian group, automorphism group, asymptotic, ▫$p$▫-group
Objavljeno: 15.10.2013; Ogledov: 2274; Prenosov: 25
URL Polno besedilo (0,00 KB)

7.
Automorphism groups of Cayley digraphs of Zp3
Edward Dobson, István Kovács, 2009, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: Cayley digraph, automorphism group
Objavljeno: 15.10.2013; Ogledov: 2118; Prenosov: 7
URL Polno besedilo (0,00 KB)
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8.
On overgroups of regular abelian p-groups
Edward Dobson, 2009, izvirni znanstveni članek

Opis: 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.
Najdeno v: osebi
Ključne besede: group theory, graph theory, Cayley graph, abelian group, regular group, p-group
Objavljeno: 15.10.2013; Ogledov: 1438; Prenosov: 24
URL Polno besedilo (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, izvirni znanstveni članek

Opis: 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]).
Najdeno v: osebi
Ključne besede: mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graph
Objavljeno: 03.04.2017; Ogledov: 747; Prenosov: 18
URL Polno besedilo (0,00 KB)

10.
Semiregular automorphisms of vertex-transitive graphs of certain valencies
Dragan Marušič, Edward Dobson, Aleksander Malnič, Lewis A. Nowitz, 2007, izvirni znanstveni članek

Opis: 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]).
Najdeno v: osebi
Ključne besede: mathematics, graph theory, transitive permutation group, 2-closed group, semiregular automorphism, vertex-transitive graph
Objavljeno: 03.04.2017; Ogledov: 715; Prenosov: 13
URL Polno besedilo (0,00 KB)

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