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Existence of non-Cayley Haar graphs
Yan-Quan Feng, István Kovács, Jie Wang, Da-Wei Yang, 2020, original scientific article

Keywords: graph, Cayley graph, Haar graph
Published in RUP: 17.06.2020; Views: 1167; Downloads: 98
URL Link to full text

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On groups all of whose Haar graphs are Cayley graphs
Yan-Quan Feng, István Kovács, Da-Wei Yang, 2019, original scientific article

Keywords: graph automorphism, Cayley graph, Haar graph
Published in RUP: 28.06.2019; Views: 1787; Downloads: 340
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On isomorphism and multiplier inequivalence of cyclic steiner quadruple systems
Edward Dobson, Tao Feng, Derek F. Holt, Patric R. J. Östergård, 2018, published scientific conference contribution abstract (invited lecture)

Keywords: isomorphism, cyclic Steiner quadruple system, automorphism
Published in RUP: 07.02.2018; Views: 2803; Downloads: 33
URL Link to full text

8.
Elementary abelian groups of rank 5 are DCI-groups
István Kovács, Yan-Quan Feng, 2018, published scientific conference contribution abstract (invited lecture)

Keywords: elementary abelian group, rank, DCI-group
Published in RUP: 07.02.2018; Views: 2202; Downloads: 78
URL Link to full text

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On 2-fold covers of graphs
Yan-Quan Feng, Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, 2008, original scientific article

Abstract: A regular covering projection ▫$\wp : \widetilde{X} \to X$▫ of connected graphs is ▫$G$▫-admissible if ▫$G$▫ lifts along ▫$\wp$▫. Denote by ▫$\tilde{G}$▫ the lifted group, and let CT▫$(\wp)$▫ be the group of covering transformations. The projection is called ▫$G$▫-split whenever the extension ▫{$\mathrm{CT}}(\wp) \to \tilde{G} \to G$▫ splits. In this paper, split 2-covers are considered, with a particular emphasis given to cubic symmetric graphs. Supposing that ▫$G$▫ is transitive on ▫$X$▫, a ▫$G$▫-split cover is said to be ▫$G$▫-split-transitive if all complements ▫$\tilde{G} \cong G$▫ of CT▫$(\wp)$▫ within ▫$\tilde{G}$▫ are transitive on ▫$\widetilde{X}$▫; it is said to be ▫$G$▫-split-sectional whenever for each complement ▫$\tilde{G}$▫ there exists a ▫$\tilde{G}$▫-invariant section of ▫$\wp$▫; and it is called ▫$G$▫-split-mixed otherwise. It is shown, when ▫$G$▫ is an arc-transitive group, split-sectional and split-mixed 2-covers lead to canonical double covers. Split-transitive covers, however, are considerably more difficult to analyze. For cubic symmetric graphs split 2-cover are necessarily canonical double covers (that is, no ▫$G$▫-split-transitive 2-covers exist) when ▫$G$▫ is 1-regular or 4-regular. In all other cases, that is, if ▫$G$▫ is ▫$s$▫-regular, ▫$s=2,3$▫ or ▫$5$▫, a necessary and sufficient condition for the existence of a transitive complement ▫$\tilde{G}$▫ is given, and moreover, an infinite family of split-transitive 2-covers based on the alternating groups of the form ▫$A_{12k+10}$▫ is constructed. Finally, chains of consecutive 2-covers, along which an arc-transitive group ▫$G$▫ has successive lifts, are also considered. It is proved that in such a chain, at most two projections can be split. Further, it is shown that, in the context of cubic symmetric graphs, if exactly two of them are split, then one is split-transitive and the other one is either split-sectional or split-mixed.
Keywords: graph theory, graphs, cubic graphs, symmetric graphs, ▫$s$▫-regular group, regular covering projection
Published in RUP: 15.10.2013; Views: 3517; Downloads: 34
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