×

zbMATH — the first resource for mathematics

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.

MSC:
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C40 Connectivity
PDF BibTeX XML Cite
Full Text: DOI arXiv Link
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.