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Enumerating Unlabelled Embeddings of Digraphs

  • Yichao Chen (a1), Xiaojian Gao (a2) and Yuanqiu Huang (a3)
Abstract

A 2-cell embedding of an Eulerian digraph D into a closed surface is said to be directed if the boundary of each face is a directed closed walk in D. In this paper, a method is developed with the purpose of enumerating unlabelled embeddings for an Eulerian digraph. As an application, we obtain explicit formulas for the number of unlabelled embeddings of directed bouquets of cycles Bn , directed dipoles OD2n and for a class of regular tournaments T 2n+1.

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[1] Bonetta-Martin, K. and McCourt, T. A., On which groups can arise as the canonical group of a spherical latin bitrade. Ars Math. Contemp. 13 (2017), 167185.
[2] Bonnington, C. P., Conder, M., Morton, M., and McKenna, P., Embedding digraphs on orientable surfaces. J. Combin. Theory Ser. B 85 (2002), 120. http://dx.doi.Org/10.1OO6/jctb.2OO1.2085.
[3] Chen, Y., Gross, J. L., and Hu, X., Enumeration of digraph embeddings. European J. Combin. 36 (2014), 660678. http://dx.doi.Org/10.1016/j.ejc.2013.10.003.
[4] Farr, G. E., Minorsfor alternating dimaps. arxiv:1311.2783.
[5] Feng, Y.-Q., Kwak, J.-H., and Zhou, J., Congruence classes of orientable 2-cell embeddings of bouquets of circles and dipoles. Electron. J. Combin. 17(2010), Research Paper 41,15.
[6] Kwak, J. H. and Lee, J., Enumeration of graph embeddings. Discrete Math. 135 (1994), 129151. http://dx.doi.org/10.1016/0012-365X(93)E0075-F
[7] Kim, J. H. and Park, Y. K., Incongruent embeddings ofa bouquet into surfaces. Bull. Austral. Math. Soc. 61 (2000), 8996. http://dx.doi.org/10.1017/S0004972700022048.
[8] Kim, J. H., Kim, H. K., and Lim, D. K., Enumerating embeddings of a dartboard graph into surfaces. Comm. Korean Math. Soc. 11 (1996), 10951104.
[9] McCourt, T. A., Growth rates ofgroups associated withface 2-coloured triangulations and directed eulerian digraphs on the sphere. Electron. J. Combin. 23(2016), no. 1, Paper 1.51, 23.
[10] McKay, B. D., The asymptotic numbers of regulär tournaments, Eulerian digraphs and Eulerian orientedgraphs. Combinatorica 10 (1990), 367377. http://dx.doi.org/10.1007/BF02128671.
[11] Moon, J. W., Tournaments with a given automorphism group. Canad. J. Math. 16 (1964), 485489. http://dx.doi.Org/10.41 53/CJM-1964-050-9.
[12] Mull, B. M., Enumerating the orientable 2-cell imbeddings ofcomplete bipartite graphs. J. Graph “Iheory 103 (1999), 7790. http://dx.doi.Org/10.1002/(SICI)1097-011 8(1 99902)30:2<77::AID-JCT2>3.0.CO;2-W
[13] Mull, B. M., Rieper, R. G., and White, A. T., Enumerating 2-cell imbeddings of connected graphs. Proc. Amer. Math. Soc. 103 (1988), 321330. http://dx.doi.Org/10.2307/2047573.
[14] Tutte, W. T., The dissection of equilateral triangles into equilateral triangles. Proc. Cambridge Phil. Soc. 44 (1948), 463482. http://dx.doi.Org/10.1017/S030500410002449X
[15] Tutte, W. T., Duality and trinity. Infinite andfinite sets (Colloq., Keszthely, 1973; dedicated to P. Erdös on his 60th birthday), Vol. III. Colloq. Math. Soc. Jänos Bolyai, 10, North-Holland, Amsterdam, 1975, pp. 1459-1472.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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