Iskanje po repozitoriju

Ključne besede: (un)directed Cayley graph, cyclic group, (un)directed circulant graph, Cayley isomorphism, (un)directed CI-graph, (D)CI-group, m-(D)CI-group, key, generalised multiplier
Objavljeno v RUP: 11.09.2023; Ogledov: 758; Prenosov: 15
Celotno besedilo (520,27 KB)

Ključne besede: graphs, automorphism group, symmetry, locally arc-transitive graphs, symmetric graphs, cycle structure, linking ring structure
Objavljeno v RUP: 02.01.2022; Ogledov: 1140; Prenosov: 19
Celotno besedilo (397,55 KB)

Opis: 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.
Ključne besede: algorithm, graph, group extension, lifting automorphisms, regular covering projection, voltages
Objavljeno v RUP: 02.01.2022; Ogledov: 978; Prenosov: 18
Celotno besedilo (317,95 KB)

Opis: 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.
Ključne besede: covering projection, graph, group extension, lifting automorphisms, voltage assignment
Objavljeno v RUP: 30.12.2021; Ogledov: 1320; Prenosov: 4
Celotno besedilo (365,16 KB)

Ključne besede: cubic graph, k-multicirculant, arc-transitive, soluble group
Objavljeno v RUP: 25.10.2021; Ogledov: 1312; Prenosov: 21
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