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31.
On strongly regular bicirculants
Dragan Marušič, Aleksander Malnič, Primož Šparl, 2007, izvirni znanstveni članek

Opis: An ▫$n$▫-bicirculantis a graph having an automorphism with two orbits of length ▫$n$▫ and no other orbits. This article deals with strongly regular bicirculants. It is known that for a nontrivial strongly regular ▫$n$▫-bicirculant, ▫$n$▫ odd, there exists a positive integer m such that ▫$n=2m^2+2m+1▫$. Only three nontrivial examples have been known previously, namely, for ▫$m=1,2$▫ and 4. Case ▫$m=1$▫ gives rise to the Petersen graph and its complement, while the graphs arising from cases ▫$m=2$▫ and ▫$m=4$▫ are associated with certain Steiner systems. Similarly, if ▫$n$▫ is even, then ▫$n=2m^2$▫ for some ▫$m \ge 2$▫. Apart from a pair of complementary strongly regular 8-bicirculants, no other example seems to be known. A necessary condition for the existence of a strongly regular vertex-transitive ▫$p$▫-bicirculant, ▫$p$▫ a prime, is obtained here. In addition, three new strongly regular bicirculants having 50, 82 and 122 vertices corresponding, respectively, to ▫$m=3,4$▫ and 5 above, are presented. These graphs are not associated with any Steiner system, and together with their complements form the first known pairs of complementary strongly regular bicirculants which are vertex-transitive but not edge-transitive.
Najdeno v: ključnih besedah
Ključne besede: mathematics, graph theory, graph, circulant, bicirculant, automorphism group
Objavljeno: 03.04.2017; Ogledov: 1016; Prenosov: 45
URL Polno besedilo (0,00 KB)

32.
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: ključnih besedah
Povzetek najdenega: ...prime, admitting a transitive action of a ▫$\{2,p\}$▫- group, has a non-identity semiregular automorphism. As a...
Ključne besede: mathematics, graph theory, transitive permutation group, 2-closed group, semiregular automorphism, vertex-transitive graph
Objavljeno: 03.04.2017; Ogledov: 819; Prenosov: 41
URL Polno besedilo (0,00 KB)

33.
Semisymmetric elementary abelian covers of the Möbius-Kantor graph
Aleksander Malnič, Štefko Miklavič, Primož Potočnik, Dragan Marušič, 2007, izvirni znanstveni članek

Opis: Let ▫$\wp_N : \tilde{X} \to X$▫ be a regular covering projection of connected graphs with the group of covering transformations isomorphic to ▫$N$▫. If ▫$N$▫ is an elementary abelian ▫$p$▫-group, then the projection ▫$\wp_N$▫ is called ▫$p$▫-elementary abelian. The projection ▫$\wp_N$▫ is vertex-transitive (edge-transitive) if some vertex-transitive (edge-transitive) subgroup of Aut ▫$X$▫ lifts along ▫$\wp_N$▫, and semisymmetric if it is edge- but not vertex-transitive. The projection ▫$\wp_N$▫ is minimal semisymmetric if ▫$\wp_N$▫ cannot be written as a composition ▫$\wp_N = \wp \circ \wp_M$▫ of two (nontrivial) regular covering projections, where ▫$\pw_M$▫ is semisymmetric. Finding elementary abelian covering projections can be grasped combinatorially via a linear representation of automorphisms acting on the first homology group of the graph. The method essentially reduces to finding invariant subspaces of matrix groups over prime fields (see [A. Malnic, D. Marušic, P. Potocnik, Elementary abelian covers of graphs, J. Algebraic Combin. 20 (2004) 71-97]). In this paper, all pairwise nonisomorphic minimal semisymmetric elementary abelian regular covering projections of the Möbius-Kantor graph, the Generalized Petersen graph GP(8,3), are constructed. No such covers exist for ▫$p=2$▫. Otherwise, the number of such covering projections is equal to ▫$(p-1)/4$▫ and ▫$1+(p-1)/4$▫ in cases ▫$p \equiv 5,9,13,17,21 \pmod{24}$▫ and ▫$p \equiv 1 \pmod{24}$▫, respectively, and to ▫$(p+1)/4$▫ and ▫$1+(p+1)/4$▫ in cases ▫$p \equiv 3,7,11,15,23 \pmod{24}$▫ and ▫$p \equiv 19 \pmod{24}$▫, respectively. For each such covering projection the voltage rules generating the corresponding covers are displayed explicitly.
Najdeno v: ključnih besedah
Povzetek najdenega: ...covering projection of connected graphs with the group of covering transformations isomorphic to ▫$N$▫. If...
Ključne besede: mathematics, graph theory, graph, covering projection, lifting automorphisms, homology group, group representation, matrix group, invariant subspaces
Objavljeno: 03.04.2017; Ogledov: 758; Prenosov: 45
URL Polno besedilo (0,00 KB)

34.
Groups that are transitive on all partitions of a given shape
Edward Dobson, Aleksander Malnič, 2015, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...transitive group, ordered partition, unordered partition, Johnson graph, Cayley...
Ključne besede: transitive group, ordered partition, unordered partition, Johnson graph, Cayley graph
Objavljeno: 03.04.2017; Ogledov: 772; Prenosov: 85
URL Polno besedilo (0,00 KB)

35.
On the order of Borel subgroups of group amalgams and an application to locally-transitive graphs
Gabriel Verret, Pablo Spiga, Luke Morgan, 2015, izvirni znanstveni članek

Najdeno v: ključnih besedah
Ključne besede: locally-restrictive, locally-transitive graph, semiprimitive, group amalgams
Objavljeno: 03.04.2017; Ogledov: 633; Prenosov: 83
URL Polno besedilo (0,00 KB)

36.
Cayley graphs on abelian groups
Gabriel Verret, Edward Dobson, Pablo Spiga, 2015, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...Cayley graph, abelian group, automorphism, ...
Ključne besede: Cayley graph, abelian group, automorphism
Objavljeno: 03.04.2017; Ogledov: 683; Prenosov: 81
URL Polno besedilo (0,00 KB)

37.
Quotients of CI-Groups are CI-Groups
Edward Dobson, Joy Morris, 2015, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...CI- group, Cayley graph, Quotient, ...
Ključne besede: CI-group, Cayley graph, Quotient
Objavljeno: 03.04.2017; Ogledov: 552; Prenosov: 89
URL Polno besedilo (0,00 KB)

38.
Določeni razredi (hiper)grafov in njihove algebraične lastnosti
Paweł Petecki, 2016, doktorska disertacija

Najdeno v: ključnih besedah
Povzetek najdenega: ...cycle, decomposition, double generalized Petersen graph, automorphism group, vertex-transitive, sign graph, L-eigenvalue, lollipop graph, ...
Ključne besede: hypergraph, hamiltonian cycle, decomposition, double generalized Petersen graph, automorphism group, vertex-transitive, sign graph, L-eigenvalue, lollipop graph
Objavljeno: 09.08.2016; Ogledov: 1382; Prenosov: 3
URL Polno besedilo (0,00 KB)

39.
Further restrictions on the structure of finite DCI-groups
Edward Dobson, Joy Morris, Pablo Spiga, 2015, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...isomorphism problem, CI- group, dihedral group, Cayley graph, ...
Ključne besede: isomorphism problem, CI-group, dihedral group, Cayley graph
Objavljeno: 08.08.2016; Ogledov: 920; Prenosov: 22
URL Polno besedilo (0,00 KB)

40.
On colour-preserving automorphisms of Cayley graphs
Klavdija Kutnar, Ademir Hujdurović, Edward Dobson, Dave Witte Morris, Joy Morris, 2016, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ...Cayley graph, automorphism, group, colouring, ...
Ključne besede: Cayley graph, automorphism, group, colouring
Objavljeno: 08.08.2016; Ogledov: 974; Prenosov: 45
URL Polno besedilo (0,00 KB)

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