Lifting Graph Automorphisms by Voltage Assignments

European Journal of Combinatorics

Volumn 21, Issue 7, 2000, Pages 927-947

  Malnič, Aleksander ^a   Nedela, Roman ^b   Škoviera, Martin ^c  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

^b MATEJ BEL UNIVERSITY   (Slovakia)

^c Faculty of Natural Sciences   (Slovakia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034404457     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1006/eujc.2000.0390     Document Type: Article

References (41)

1. D. Archdeacon, P. Gvozdjak and J. Širáň, Constructing and forbidding automorphisms in lifted maps, Math. Slovaca, 47 (1997), 113-129.
2. D. Archdeacon, R. B. Richter, J. Širáň and M. Škoviera, Branched coverings of maps and lifts of map homomorphisms, Aust. J. Comb., 9 (1994), 109-121.
3. M. A. Armstrong, Lifting group actions to covering spaces, in: Discrete Groups and Geometry, London Mathematical Society Lecture Notes 173, W. J. Harwey and C. Maclachlan (eds), Cambridge University Press, Cambridge, 1992, pp. 10-15.
4. N. L. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, 1974.
5. N. L. Biggs, Homological coverings of graphs, J. London Math. Soc., 30 (1984), 1-14.
6. J. S. Birman and H. M. Hilden, Lifting and projecting homeomorphisms, Arch. Math., 23 (1972), 428-434.
7. D. Ž. Djoković, Automorphisms of graphs and coverings, J. Comb. Theory, Ser. B, 16 (1974), 243-247.
8. S.-F. Du, D. Marušič and A. O. Waller, On 2-arc transitive covers of complete graphs, J. Combin. Theory, 74 (1998), 276-290.
9. A. Gardiner and C. E. Praeger, A geometrical approach to imprimitive graphs, Proc. London Math. Soc., 71 (1995), 524-546.
10. J. L. Gross, Voltage graphs, Discrete Math., 9 (1974), 239-246.
11. J. L. Gross and S. R. Alpert, The topological theory of current graphs, J. Comb. Theory, Ser. B, 17 (1974), 218-233.
12. J. L. Gross and T. W. Tucker, Generating all graph coverings by permutation voltage assignments, Discrete Math., 18 (1977), 273-283.
13. J. L. Gross and T. W. Tucker, Topological Graph Theory, Wiley-Interscience, New York, 1987.
14. P. Gvozdjak and J. Širáň, Regular maps from voltage assignments, in: Graph Structure Theory, Contemporary Mathematics (AMS Series) 147, N. Robertson and P. Seymour (eds), 1993, pp. 441-454.
15. M. Hofmeister, Isomorphisms and automorphisms of graph coverings, Discrete Math., 98 (1991), 175-183.
16. G. A. Jones and D. Singerman, Theory of maps on orientable surfaces, Proc. London Math. Soc., 37 (1978), 273-307.
17. J. H. Kwak and J. Lee, Isomorphism classes of graph bundles, Can. J. Math., 4 (1990), 747-761.
18. J. H. Kwak and J. Lee, Counting some finite-fold coverings of a graph, Graphs Comb., 8 (1992), 277-285.
19. A. M. MacBeath, On a theorem of Hurwitz, Proc. Glasgow Math. Assoc., 5 (1961), 90-96.
20. A. Malnič, Group actions, coverings and lifts of automorphisms, Discrete Math., 182 (1998), 203-218.
21. A. Malnič, On the structure of lifted groups, in preparation.
22. A. Malnič and D. Marušič, Imprimitive groups and graph coverings, in: Coding Theory, Design Theory, Graph Theory: Proc. M. Hall Memorial Conf., D. Jungnickel and S. A. Vanstone (eds), J. Wiley and Sons, New York, 1993, pp. 221-229.
23. A. Malnič, D. Marušič and N. Seifter, Constructing infinite one-regular graphs, Europ. J. Combin., 20 (1999), 845-853.
24. A. Malnič, R. Nedela and M. Škoviera, Regular homomorphisms and regular maps, submitted.
25. D. Marušič and R. Nedela, On the point stabilizers of transitive groups with non-self-paired suborbits of length 2, submitted.
26. k), J. Comb. Theory, Ser. B, 58 (1993), 46-57.
27. W. S. Massey, Algebraic Topology: An Introduction, Harcourt Brace and World, Heidelberg, Berlin, 1967.
28. R. Nedela and M. Skoviera, Regular maps of canonical double coverings of graphs, J. Comb. Theory, Ser. B, 67 (1996), 249-277.
29. R. Nedela and M. Škoviera, Regular maps from voltage assignments and exponent groups, Europ. J. Combinatorics, 18 (1997), 807-823.
30. R. Nedela and M. Škoviera, Exponents of orientable maps, Proc. London Math. Soc., 75 (1997), 1-31.
31. T. Pisanski and J. Vrabec, Graph bundles, Preprint Series, Department of Mathematics, University of Ljubljana, 20 (1982), 213-298.
32. G. Ringel, Map Color Theorem, Springer-Verlag, Berlin, 1974.
33. D. J. S. Robinson, A Course in Theory of Groups, Graduate Texts in Mathematics 80, Springer-Verlag, New York, Heidelberg, Berlin, 1982.
34. N. Seifter and V. Trofimov, Automorphism groups of covering graphs, J. Comb. Theory, Ser. B, 71 (1997), 67-72.
35. N. Steenrod, The Topology of Fibre Bundles, Princeton University Press, Princeton, NJ, 1951.
36. D. B. Surowski, Covers of simplicial complexes and applications to geometry, Geom. Dedicata, 16 (1984), 35-62.
37. D. B. Surowski, Lifting map automorphisms and MacBeath's theorem, J. Comb. Theory, Ser. B, 50 (1988), 135-149.
38. M. Škoviera, A contribution to the theory of voltage graphs, Discrete Math., 61 (1986), 281-292.
39. A. Venkatesh, Graph coverings and group liftings, submitted.
40. A. T. White, Graphs, Groups, and Surfaces, North-Holland, Amsterdam, 1984.
41. H. Zieschang, Lifting and projecting homeomorphisms, Arch. Math., 24 (1973), 416-421.