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The planar cubic Cayley graphs of connectivity 2. (English) Zbl 1365.05123
Summary: We classify the planar cubic Cayley graphs of connectivity 2, providing an explicit presentation and embedding for each of them. Combined with the paper of the author [“The planar cubic Cayley graphs”, Preprint, arXiv:1102.2087 ] this yields a complete description of all planar cubic Cayley graphs.

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C40 Connectivity
Full Text: DOI arXiv Link
[1] Babai, L., Automorphism groups, isomorphism, reconstruction, (Graham et al., R. L., Handbook of Combinatorics, Vol. 2, (1995), Elsevier (North-Holland) Amsterdam), 1447-1540 · Zbl 0846.05042
[2] Bogopolski, O., Introduction to Group Theory, (2008), EMS Zuerich, Switzerland
[3] Bonnington, C. P.; Watkins, M. E., Planar embeddings with infinite faces, J. Graph Theory, 42, 4, 257-275, (2003) · Zbl 1023.05036
[4] Cui, Q.; Wang, J.; Yu, X., Hamilton circles in infinite planar graphs, J. Combin. Theory Ser. B, 99, 1, 110-138, (2009) · Zbl 1193.05117
[5] Diestel, Reinhard, Graph Theory, (2005), Springer-Verlag, Electronic edition available at: http://www.math.uni-hamburg.de/home/diestel/books/graph.theory
[6] Droms, C., Infinite-ended groups with planar Cayley graphs, J. Group Theory, 9, 4, 487-496, (2006) · Zbl 1099.20017
[7] Droms, C.; Servatius, B.; Servatius, H., Connectivity and planarity of Cayley graphs, Beitr. Algebra Geom., 39, 2, 269-282, (1998) · Zbl 0917.05036
[8] M.J. Dunwoody, Planar graphs and covers, 2009. Preprint available at http://www.personal.soton.ac.uk/mjd7/
[9] Georgakopoulos, A., Characterising planar Cayley graphs and Cayley complexes in terms of group presentations, European J. Combin., 36, 282-293, (2014) · Zbl 1284.05123
[10] A. Georgakopoulos, The planar cubic Cayley graphs, Mem. Amer. Math. Soc., in press · Zbl 1353.05002
[11] A. Georgakopoulos, M. Hamann, The planar Cayley graphs are effectively enumerable, 2015, arXiv:150603361
[12] Kozma, G., Percolation, perimetry, planarity, Rev. Mat. Iberoam., 23, 2, 671-676, (2007) · Zbl 1131.60087
[13] Whitney, H., Congruent graphs and the connectivity of graphs, Amer. J. Math., 54, 1, 150-168, (1932) · JFM 58.0609.01
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