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Testing whether the lifted group splits
Rok Požar, 2016, original scientific article

Abstract: Let a group of automorphisms lift along a regular covering projection of connected graphs given combinatorially by means of voltages. The data that determine the lifted group and its action are then conveniently encoded in terms of voltages as well. Along these lines, an algorithm for testing whether the lifted group is a split extension of the group of covering transformations has recently been proposed in the case when the group of covering transformations is solvable. It consists of decomposing the covering into a series of coverings with elementary abelian groups of covering transformations, and inductively solving the problem at every elementary abelian step. Although the explicit construction of the lifted group is not needed, it still involves time and space consuming constructions of certain subgroups in the lifted group at every step except at the final one. In this paper, an improved version that completely avoids such constructions is presented. From voltage distribution we first compute the weak action and the factor set that determine the lifted group, and we then carry out the test by extracting the necessary information only from the corresponding weak actions and factor sets at every step. An experimental comparison is made against the previous version.
Keywords: algorithm, graph, group extension, lifting automorphisms, regular covering projection, voltages
Published in RUP: 03.01.2022; Views: 707; Downloads: 17
.pdf Full text (317,95 KB)

3.
The automorphism groups of non-edge transitive rose window graphs
Edward Dobson, István Kovács, Štefko Miklavič, 2015, original scientific article

Abstract: In this paper, we determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we determine the isomorphism classes of non-edge-transitive rose window graphs.
Keywords: rose window graphs, automorphism group, isomorphism problem, vertex-transitive graph
Published in RUP: 31.12.2021; Views: 879; Downloads: 18
.pdf Full text (275,74 KB)

4.
Sectional split extensions arising from lifts of groups
Rok Požar, 2013, original scientific article

Abstract: Covering techniques have recently emerged as an effective tool used for classification of several infinite families of connected symmetric graphs. One commonly encountered technique is based on the concept of lifting groups of automorphisms along regular covering projections ▫$\wp \colon \tilde{X} \to X$▫. Efficient computational methods are known for regular covers with cyclic or elementary abelian group of covering transformations CT▫$(\wp)$▫. In this paper we consider the lifting problem with an additional condition on how a group should lift: given a connected graph ▫$X$▫ and a group ▫$G$▫ of its automorphisms, find all connected regular covering projections ▫$\wp \colon \tilde{X} \to X$▫ along which ▫$G$▫ lifts as a sectional split extension. By this we mean that there exists a complement ▫$\overline{G}$▫ of CT▫$(\wp)$▫ within the lifted group ▫$\tilde{G}$▫ such that ▫$\overline{G}$▫ has an orbit intersecting each fibre in at most one vertex. As an application, all connected elementary abelian regular coverings of the complete graph ▫$K_4$▫ along which a cyclic group of order 4 lifts as a sectional split extension are constructed.
Keywords: covering projection, graph, group extension, lifting automorphisms, voltage assignment
Published in RUP: 31.12.2021; Views: 988; Downloads: 3
.pdf Full text (365,16 KB)

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A family of non-Cayley cores that are constructed from vertex-transitive or strongly regular self-complementary graphs
Marko Orel, 2021, published scientific conference contribution abstract

Keywords: cores, graph homomorphisms, automorphism group, self-complementary graphs
Published in RUP: 30.07.2021; Views: 983; Downloads: 73
URL Link to full text
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8.
A family of non-Cayley cores that are constructed from vertex-transitive or strongly regular self-complementary graphs
Marko Orel, 2021, published scientific conference contribution abstract

Keywords: cores, graph homomorphisms, automorphism group, self-complementary graphs
Published in RUP: 30.07.2021; Views: 1192; Downloads: 42
.pdf Full text (1,01 MB)
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Bicirculants via imprimitivity block systems
Dragan Marušič, 2021, original scientific article

Keywords: semiregular group, imprimitive group, arc-transitive graph, bicirculant
Published in RUP: 06.05.2021; Views: 796; Downloads: 30
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