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Title Regular maps with nilpotent automorphism groups Author info Aleksander Malnic, Roman Nedela, Martin Škoviera Author Malnič Aleksander (34%)
Co-authors Nedela Roman 1960- (33%) UMBFP12 - Inštitút matematiky a informatiky
Škoviera Martin (33%)
Source document European Journal of Combinatorics. Vol. 33, no. 8 (2012), pp. 1974-1986. - London : Academic Press, 2012 Keywords matematika - mathematics grafy - charts - graphs regulárne mapy regular maps Language English Country Great Britian systematics 51 Annotation We study regular maps with nilpotent automorphism groups in detail. We prove that every nilpotent regular map decomposes into a direct product of maps H x K, where Aut (H) is a 2-group and K is a map with a single vertex and an odd number of semiedges. Many important properties of nilpotent maps follow from this canonical decomposition, including restrictions on the valency, covalency, and the number of edges. We also show that, apart from two well-defined classes of maps on at most two vertices and their duals, every nilpotent regular map has both its valency and covalency divisible by 4. Finally, we give a complete classification of nilpotent regular maps of nilpotency class 2. Public work category ADE No. of Archival Copy 28518 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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Title Planar width of regular maps Author info Martin Mačaj, Jozef Širáň, Mária Ipolyiová Author Mačaj Martin (33%)
Co-authors Širáň Jozef (33%)
Grausová Mária 1976- (34%) UMBEF05 - Katedra kvantitatívnych metód a informačných systémov
Source document Electronic Notes in Discrete Mathematics : 6th Czech-Slovak International Symposium on Combinatorics, Graph Theory, Algorithms and Applications, Prague, Czech Republic, 10. - 16.7.2006. Vol. 28, No. March (2007), pp. 477-484. - : Elsevier, 2007 Keywords regulárne mapy planárna šírka regular maps planar width Language English systematics 511 Public work category AFC No. of Archival Copy 4823 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ article
Title A classification of regular embeddings of graphs of order a product of two primes Author info S. F. Du, J. H. Kwak, R. Nedela Author Du Shaofei (34%)
Co-authors Kwak Jin Ho (33%)
Nedela Roman 1960- (33%) UMBFP12 - Inštitút matematiky a informatiky
Source document Journal of Algebraic Combinatorics. Vol. 19, no. 2 (2004), pp. 123-141. - New York : Springer, 2004 Keywords matematika - mathematics regulárne mapy grafy - charts - graphs regular maps Language English Country Netherlands systematics 51 Annotation In this paper, we classify the regular embeddings of arc-transitive simple graphs of order pq for any two primes p and q (not necessarily distinct) into orientable surfaces. Our classification is obtained by direct analysis of the structure of arc-regular subgroups (with cyclic vertex-stabilizers) of the automorphism groups of such graphs. This work is independent of the classification of primitive permutation groups of degree p or degree pq for p not equal q and it is also independent of the classification of the arc-transitive graphs of order pq for p not equal q. Public work category ADE No. of Archival Copy 28528 Repercussion category ZHOU, Jin Xin - FENG, Yan Quan. Regular maps of graphs of order 4p. In Acta mathematica sinica. ISSN 1439-8516, 2012, vol. 28, no. 5, pp. 989-1012.
HARTLEY, Michael I. - HUBARD, Isabel - LEEMANS, Dimitri. Two atlases of abstract chiral polytopes for small groups. In Ars mathematica contemporanea. ISSN 1855-3966, 2012, vol. 5, no. 2, pp. 371-382.
D´AZEVEDO, Antonio Breda - FERNANDES, Maria Elisa. Classification of primer hypermaps with a prime number of hyperfaces. In European journal of combinatorics. ISSN 0195-6698, 2011, vol. 32, no. 2, pp. 233-242.
XU, Jing. A classification of regular embeddings of hypercubes Q (2m) with m odd. In Science in China series A-mathematics. ISSN 1006-9283, 2007, vol. 50, no. 12, pp. 1673-1679.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article
Title Half-arc-transitive graphs and chiral hypermaps Author info A. B. D´Azevedo, R. Nedela Author Breda d'Azevedo Antonio (50%)
Co-authors Nedela Roman 1960- (50%) UMBFP12 - Inštitút matematiky a informatiky
Source document European Journal of Combinatorics. Vol. 25, no. 3 (2004), pp. 423-436. - London : Academic Press, 2004 Keywords matematika - mathematics grafy - charts - graphs regulárne mapy regular maps Language English Country Great Britian systematics 51 Annotation A subgroup G of automorphisms of a graph X is said to be 1/2-arc-transitive if it is vertex- and edge- but not arc-transitive. The graph X is said to be 1/2-arc-transitive if Aut X is 1/2-arc-transitive. The interplay of two different concepts, maps and hypermaps on one side and 1/2-arc-transitive group actions on graphs on the other, is investigated. The correspondence between regular maps and 1/2-arc-transitive group actions on graphs of valency 4 given via the well known concept of medial graphs (European J. Combin. 19 (1998) 345) is generalised. Any orientably regular hypermap R gives rise to a uniquely determined medial map whose underlying graph Y admits a 1/2-arc-transitive group action of the automorphism group G of the original hypermap R. Moreover, the vertex stabiliser of the action of G on Y is cyclic. On the other hand, given graph X and G less than or equal to Ant X acting 1/2-arc-transitively with a cyclic vertex stabiliser, we can construct an orientably regular hyperma Public work category ADE No. of Archival Copy 28527 Repercussion category WANG, Xiuyun - FENG, Yan-Quan. There exists no tetravalent half-arc-transitive graph of order 2p(2). In Discrete mathematics. ISSN 0012-365X, 2010, vol. 310, no. 12, pp. 1721-1724.
SPARL, Primoz. On the classification of quartic half-arc-transitive metacirculants. In Discrete mathematics. ISSN 0012-365X, 2009, vol. 309, no. 8, pp. 2271-2283.
MARUSIC, Dragan - SPARL, Primoz. On quartic half-arc-transitive metacirculants. In Journal of algebraic combinatorics. ISSN 0925-9899, 2008, vol. 28, no. 3, pp. 365-395.
SPARL, Primoz. A classification of tightly attached half-arc-transitive graphs of valency 4. In Journal of combinatorial theory series B. ISSN 0095-8956, 2008, vol. 98, no. 5, pp. 1076-1108.
FENG, Yan-Quan - KWAK, Jin Ho - ZHOU, Chuixiang. Constructing even radius tightly attached half-arc-transitive graphs of valency four. In Journal of algebraic combinatorics. ISSN 0925-9899, 2007, vol. 26, no. 4, pp. 431-451.
ZHOU, Chuixiang - FENG, Yan-Quan. An infinite family of tetravalent half-arc-transitive graphs. In Discrete mathematicsISCRETE MATHEMATICS. ISSN 0012-365X, 2006, vol. 306, no. 18, pp. 2205-2211.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article
Title Regular embeddings of complete bipartite graphs Author info R. Nedela, M. Skoviera, A. Zlatos Author Nedela Roman 1960- (34%) UMBFP12 - Inštitút matematiky a informatiky
Co-authors Škoviera Martin (33%)
Zlatos Andrej (33%)
Source document Dicsrete mathemtics. Vol. 258, no. 1-3 (2002), pp. 379-381. - Amsterdam : Elsevier Science, 2002 Keywords matematika - mathematics regulárne mapy grafy - charts - graphs regular maps Language English Country Netherlands systematics 51 Annotation We prove that for any prime number p the complete bipartite graph K-p,K-p has, up to isomorphism, precisely one regular embedding on an orientable surface-the well-known embedding with faces bounded by hamiltonian cycles. Public work category ADE No. of Archival Copy 28522 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, no., pp. 437-452.
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, ShaoFeo. 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, no. 2, pp. 427-453.
DU, Shao-Fei - KWAK, Jin Ho. Nonorientable regular embeddings of graphs of order p(2). In Discrete mathematics. ISSN 0012-365X, 2010, vol. 310, no. 12, pp. 1743-1751.
KNOR, Martin - SIRAN, Jozef. Regular hamiltonian embeddings of K-n,K-n and regular triangular embeddings of K-n,K-n,K-n. In Discrete mathematics. ISSN 0012-365X, 2008, vol. 308, no. 20, pp. 4796-4800.
KWAK, Jin Ho - KWON, Young Soo. Classification of reflexible regular embeddings and self-Petrie dual regular embeddings of complete bipartite graphs. In Discrete mathematics. ISSN 0012-365X, 2008, vol. 308, no. 11, pp. 2156-2166.
JONES, Gareth A. - KOOLEN, J. - KWAK, J. H. - XU, M. Y. Complete bipartite maps, factorisable groups and generalised Fermat curves. In Applications of group theory to combinatorics. Boca Raton : CRC Press - Taylor & Francis group, 2008. ISBN 978-0-415-47184-8, pp. 43-58.
KWAK, J. H. - KWON, Y. S. Regular orientable embeddings of complete bipartite graphs. In Journal of graph theory. ISSN 0364-9024, 2005, vol. 50, no. 2, pp. 105-122.
KWON, Y. S. New regular embeddings of n-cubes Qn. In Journal of graph theory. ISSN 0364-9024, 2004, vol. 46, no. 4, pp. 297-312.
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