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41.
On the full automorphism group in vertex-transitive graphs
Dragan Marušič, 2015, published scientific conference contribution abstract

Found in: ključnih besedah
Keywords: odd automorphism, automorphism group, graph
Published: 15.10.2015; Views: 805; Downloads: 13
URL Full text (0,00 KB)

42.
On the split structure of lifted groups
Aleksander Malnič, Rok Požar, 2016, original scientific article

Found in: ključnih besedah
Summary of found: ...abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems...
Keywords: algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect product
Published: 15.10.2015; Views: 991; Downloads: 54
URL Full text (0,00 KB)

43.
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: ključnih besedah
Summary of found: ...that a minimal normal subgroup of a 2-closed permutation group of square-free degree in its...
Keywords: mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graph
Published: 03.04.2017; Views: 855; Downloads: 45
URL Full text (0,00 KB)

44.
Symmetry structure of bicirculants
Boštjan Frelih, Primož Šparl, Aleksander Malnič, Dragan Marušič, 2007, original scientific article

Abstract: An ▫$n$▫-bicirculant is a graph having an automorphism with two orbits of length ▫$n$▫ and no other orbits. Symmetry properties of ▫$p$▫-bicirculants, ▫$p$▫ a prime, are extensively studied. In particular, the actions of their automorphism groups are described in detail in terms of certain algebraic representation of such graphs.
Found in: ključnih besedah
Keywords: mathematics, graph theory, graph, circulant, bicirculant, automorphism group
Published: 03.04.2017; Views: 959; Downloads: 51
URL Full text (0,00 KB)

45.
On strongly regular bicirculants
Dragan Marušič, Aleksander Malnič, Primož Šparl, 2007, original scientific article

Abstract: 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.
Found in: ključnih besedah
Keywords: mathematics, graph theory, graph, circulant, bicirculant, automorphism group
Published: 03.04.2017; Views: 1016; Downloads: 45
URL Full text (0,00 KB)

46.
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: ključnih besedah
Summary of found: ...an automorphism and, more generally, that all 2-closed transitive permutation groups contain such an element... ...prime, admitting a transitive action of a ▫$\{2,p\}$▫- group, has a non-identity semiregular automorphism. As a...
Keywords: mathematics, graph theory, transitive permutation group, 2-closed group, semiregular automorphism, vertex-transitive graph
Published: 03.04.2017; Views: 817; Downloads: 41
URL Full text (0,00 KB)

47.
Semisymmetric elementary abelian covers of the Möbius-Kantor graph
Aleksander Malnič, Štefko Miklavič, Primož Potočnik, Dragan Marušič, 2007, original scientific article

Abstract: 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.
Found in: ključnih besedah
Summary of found: ...covering projection of connected graphs with the group of covering transformations isomorphic to ▫$N$▫. If...
Keywords: mathematics, graph theory, graph, covering projection, lifting automorphisms, homology group, group representation, matrix group, invariant subspaces
Published: 03.04.2017; Views: 758; Downloads: 45
URL Full text (0,00 KB)

48.
Groups that are transitive on all partitions of a given shape
Edward Dobson, Aleksander Malnič, 2015, original scientific article

Found in: ključnih besedah
Summary of found: ...transitive group, ordered partition, unordered partition, Johnson graph, Cayley...
Keywords: transitive group, ordered partition, unordered partition, Johnson graph, Cayley graph
Published: 03.04.2017; Views: 771; Downloads: 85
URL Full text (0,00 KB)

49.
50.
Cayley graphs on abelian groups
Gabriel Verret, Edward Dobson, Pablo Spiga, 2015, original scientific article

Found in: ključnih besedah
Summary of found: ...Cayley graph, abelian group, automorphism, ...
Keywords: Cayley graph, abelian group, automorphism
Published: 03.04.2017; Views: 683; Downloads: 81
URL Full text (0,00 KB)

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