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1.
Decomposition of skew-morphisms of cyclic groups
István Kovács, Roman Nedela, 2011, original scientific article

Abstract: A skew-morphism of a group ▫$H$▫ is a permutation ▫$\sigma$▫ of its elements fixing the identity such that for every ▫$x, y \in H$▫ there exists an integer ▫$k$▫ such that ▫$\sigma (xy) = \sigma (x)\sigma k(y)$▫. It follows that group automorphisms are particular skew-morphisms. Skew-morphisms appear naturally in investigations of maps on surfaces with high degree of symmetry, namely, they are closely related to regular Cayley maps and to regular embeddings of the complete bipartite graphs. The aim of this paper is to investigate skew-morphisms of cyclic groups in the context of the associated Schur rings. We prove the following decomposition theorem about skew-morphisms of cyclic groups ▫$\mathbb Z_n$▫: if ▫$n = n_{1}n_{2}$▫ such that ▫$(n_{1}n_{2}) = 1$▫, and ▫$(n_{1}, \varphi (n_{2})) = (\varphi (n_{1}), n_{2}) = 1$▫ (▫$\varphi$▫ denotes Euler's function) then all skew-morphisms ▫$\sigma$▫ of ▫$\mathbb Z_n$▫ are obtained as ▫$\sigma = \sigma_1 \times \sigma_2$▫, where ▫$\sigma_i$▫ are skew-morphisms of ▫$\mathbb Z_{n_i}, \; i = 1, 2$▫. As a consequence we obtain the following result: All skew-morphisms of ▫$\mathbb Z_n$▫ are automorphisms of ▫$\mathbb Z_n$▫ if and only if ▫$n = 4$▫ or ▫$(n, \varphi(n)) = 1$▫.
Found in: osebi
Keywords: cyclic group, permutation group, skew-morphism, Schur ring
Published: 15.10.2013; Views: 1930; Downloads: 54
URL Full text (0,00 KB)

2.
Branched cyclic regular coverings over platonic maps
Roman Nedela, Kan Hu, Naer Wang, 2014, original scientific article

Found in: osebi
Keywords: zemljevidi, grafi, krov, maps, graphs, covering
Published: 15.10.2015; Views: 1394; Downloads: 85
URL Full text (0,00 KB)

3.
4.
6-decomposition of snarks
Roman Nedela, Ján Karabáš, Edita Máčajová, 2013, original scientific article

Found in: osebi
Keywords: dekompozicije, graf, barvanje, decompositions, graphs, coloring
Published: 15.10.2015; Views: 969; Downloads: 46
URL Full text (0,00 KB)

5.
6.
A characterization of regular embeddings of n-dimensional cubes
Roman Nedela, Domenico A. Catalano, 2010, original scientific article

Found in: osebi
Keywords: n-dimensional cubes, regular embedding, regular map
Published: 15.10.2015; Views: 804; Downloads: 44
URL Full text (0,00 KB)

7.
Regular embeddings of cycles with multiple edges revisited
Martin Škoviera, Roman Nedela, Kan Hu, Naer Wang, 2015, original scientific article

Abstract: Regularne vložitve ciklov z večkratnimi povezavami se pojavljajo v literaturi že kar nekaj časa, tako v topološki teoriji grafov kot tudi izven nje. Ta članek izriše kompletno podobo teh zemljevidov na ta način, da povsem opiše, klasificira in enumerira regularne vložitve ciklov z večkratnimi povezavami tako na orientabilnih kot tudi na neorientabilnih ploskvah. Večina rezultatov je sicer znana v tej ali oni obliki, toda tu so predstavljeni iz poenotenega zornega kota, osnovanega na teoriji končnih grup. Naš pristop daje dodatno informacijo tako o zemljevidih kot o njihovih grupah avtomorfizmov, priskrbi pa tudi dodaten vpogled v njihove odnose.
Found in: osebi
Keywords: regularna vložitev, večkratna povezava, Hölderjev izrek, Möbiusov zemljevid, regular embedding, multiple edge, Hölder's Theorem, Möbius map
Published: 15.10.2015; Views: 1041; Downloads: 53
URL Full text (0,00 KB)

8.
Classification of regular embeddings of n-dimensional cubes
Shao Fei Du, Marston D. E. Conder, Stephen Wilson, Roman Nedela, Domenico A. Catalano, Young Soo Kwon, 2011, original scientific article

Found in: osebi
Keywords: cube, classification, regular embedding
Published: 15.10.2015; Views: 1199; Downloads: 65
URL Full text (0,00 KB)

9.
Archimedean maps of higher genera
Roman Nedela, Ján Karabáš, 2012, original scientific article

Found in: osebi
Keywords: maps, graphs, embedding
Published: 03.04.2017; Views: 832; Downloads: 97
URL Full text (0,00 KB)

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