Dihedral covers of the complete graph K_5
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Abstract
A regular cover of a connected graph is called dihedral if its transformation group is dihedral. In this paper the author classifies all dihedral coverings of the complete graph $K_5$ whose fibre-preserving automorphism subgroups act arc-transitively.
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Ghasemi, M.
(2014).
Dihedral covers of the complete graph K_5.
Acta Mathematica Universitatis Comenianae, 83(2), 231-244.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/91/73
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References
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[2] D. Archdeacon, P. Gvozdnjak, J. Širáň, Constructing and forbidding automorphisms in lifted maps, Math. Slovaca 47 (1997) 113-129.
[3] Y.-Q. Feng, J.H. Kwak, Cubic symmetric graphs of order a small number times a prime or a prime square, J. Combin. Theory ser. B, 97 (2007) 627-646.
[4] Y.-Q. Feng, J.H. Kwak, Classifying cubic symmetric graphs of order 10p or 10p^2, Science in China (A) 49(3) (2006) 300-319.
[5] Y.-Q. Feng, J.H. Kwak, K.S. Wang, Classifying cubic symmetric graphs of order 8p or 8p^2, European J. Combin. 26 (2005) 1033-1052.
[6] Y.-Q. Feng, J.H. Kwak, s-regular dihedral coverings of the complete graph of order 4, Chin. Ann. Math. 25B:1 (2004), 57-64.
[7] Y.-Q. Feng, K.S. Wang, s-regular cyclic coverings of the three-dimensional hypercube Q_3, European J. Combin. 24 (2003) 719-731.
[8] Y.-Q. Feng, J.-X. Zhou, Edge-transitive dihedral or cyclic covers of cubic symmetric graphs of order 2p, submitted.
[9] J.L. Gross, T.W. Tucker, Generating all graph coverings by permutation voltage assignment, Discrete Math. 18 (1977) 273-283.
[10] Bostjan Kuzman, Arc-transitive elementary abelian covers of the complete graph K_5, Linear Algebra Appl. 433 (2010) 1909-1921.
[11] J. H. Kwak, J.M. Oh, Arc-transitive elementary abelian covers of the octahedron graph, Linear Algebra Appl. 429 (2008), 2180-2198.
[12] A. Malnic, Group actions, coverings and lifts of automorphisms, Discrete Math. 182 (1998) 203-218.
[13] A. Malnic, D. Marusic and P. Potocnik, Elementary abelian covers of graphs, J. Algebr. Combin. 20 (2004) 71-97.
[14] A. Malnic, D. Marušic and P. Potočnik, On cubic graphs admitting an edge-transitive solvable group, J. Algebr. Combin. 20 (2004) 99-113.
[15] A. Malnic, D. Marusic, P. Potocnik and C.Q. Wang, An innite family of cubic edgebut not vertex-transitive graphs, Discrete Math. 280 (2004) 133-148.
[16] M. Škoviera, A contribution to the theory of voltage groups, Discrete Math. 61 (1986) 281-292.