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Title 2-Groups that factorise as products of cyclic groups, and regular embeddings of complete bipartite graphs Author info Shaofei Du ... [et al.] Author Du Shaofei (20%)
Co-authors Jones Gareth (20%)
Kwak Jin Ho (20%)
Nedela Roman 1960- (20%) UMBFP12 - Inštitút matematiky a informatiky
Škoviera Martin (20%)
Source document Ars Mathematica Contemporanea. Vol. 6, no. 1 (2013), pp. 155-170. - Koper : Univerza na Primorskem, 2013 Keywords complete bipartite graphs product of cyclic groups regular maps Language English Country Slovenia systematics 51 Public work category ADM No. of Archival Copy 26465 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
article
Title Decomposition of skew-morphisms of cyclic groups Author info István Kovács, Roman Nedela Author Kovács István (50%)
Co-authors Nedela Roman 1960- (50%) UMBFP10 - Katedra matematiky
Source document Ars Mathematica Contemporanea. Vol. 4, no. 2 (2011), pp. 329-349. - Koper : Univerza na Primorskem, 2011 Keywords skew-morphisms product of cyclic groups decomposition Language English Country Slovenia systematics 51 Annotation A skew-morphism of a group H is a permutation a of its elements fixing the identity such that for every x, y is an element of H there exists an integer k such that sigma(xy) = sigma(x)a(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 Z(n) : if n = n(1)n(2) such that (n(1), n(2)) = 1, and (n(1), phi(n(2))) = (phi(n(1)), n(2)) = 1 (phi denotes Euler's function) then all skew-morphisms sigma of Z(n) are obtained as sigma = sigma(1) x sigma(2), where sigma(i) are skew-morphisms of Z(ni) i = 1, 2. As a consequence we obtain the following result: All skew-m [...] Public work category ADC No. of Archival Copy 20294 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article
Title Complete bipartite graphs with a unique regular embedding Author info Gareth Jones, Roman Nedela, Martin Škoviera Author Jones Gareth (34%)
Co-authors Nedela Roman 1960- (33%) UMBFP10 - Katedra matematiky
Škoviera Martin (33%)
Source document Journal of Combinatorial Theory : Series B. Vol. 98, no. 2 (2008), pp. 241-248. - San Diego : Academic Press Inc. Elsevier Science, 2008 Keywords complete bipartite graphs regular maps regular embedding orientable surface product of cyclic groups Language English Country United States of America systematics 51 Public work category ADC No. of Archival Copy 9456 Repercussion category DU, Shaofei - ZHANG, Jun-Yang. A classification of orientably-regular embeddings of complete multipartite graphs. In European journal of combinatorics. ISSN 0195-6698, 2014, vol. 36, pp. 437-452.
FAN, Wenwen - LEEMANS, Dimitri - LI, Cai Heng - PAN, Jiangmin. Locally 2-arc-transitive complete bipartite graphs. In Journal of combinatorial theory series A. ISSN 0097-3165, 2013, vol. 120, no. 3, pp. 683-699.
ZHANG, Jun-Yang - DU, Shao-Fei. On the orientable regular embeddings of complete multipartite graphs. In European journal of combinatorics. ISSN 0195-6698, 2012, vol. 33, no. 6, pp. 1303-1312.
KWAK, Jin Ho - KWON, Young Soo. Classification of nonorientable regular embeddings of complete bipartite graphs. In Journal of combinatorial theory series B. ISSN 0095-8956, 2011, vol. 101, no. 4, pp. 191-205.
WANG FURONG - DU SHAOFEI. Nonorientable regular embeddings of graphs of order pq. In Science China - Mathematics. ISSN 1674-7283, 2011, vol. 54, no. 2, pp. 351-363.
JONES, Gareth A. Regular embeddings of complete bipartite graphs : classification and enumeration. In Proceedings of the London Mathematical Society. ISSN 0024-6115, 2010, vol. 101, part 2, pp. 427-453.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article