Automorphism groups and isomorphisms of Cayley digraphs

Discrete Mathematics

Volumn 182, Issue 1-3, 1998, Pages 309-319

  Xu, Ming Yao ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

Cayley digraphs; CI subsets of a group; Normal Cayley digraphs

Indexed keywords

EID: 0000705841     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(97)00152-0     Document Type: Article

References (39)

1. B. Alspach, M. Conder, D. Marušič, M.Y. Xu, Two-arc-transitive circulants, J. Algebraic Combin. 5 (1996) 83-86.
2. B. Alspach, M.Y. Xu, 1/2-transitive graphs of order 3p, J. Algebraic Combin. 3 (1994) 347-355.
3. L. Babai, Isomorphism problem for a class of point-symmetric structures, Acta Math. Acad. Sci. Hungar. 29 (1977) 329-336.
4. L. Babai, Finite digraphs with regular automorphism groups, Period. Math. Hungar. 11 (1980) 257-270.
5. L. Babai, On the abstract group of automorphisms, in: H.N.V. Temperley Combinatorics (Ed.), London Math. Soc, Lecture Note Series 52, 1981, pp. 1-40.
6. L. Babai, P. Frankl, Isomorphisms of Cayley graphs I, Colloq. Math. Soc. J. Bolyai, 18. Combinatorics, Keszthely, 1976; North-Holland, Amsterdam, 1978, pp. 35-52.
7. L. Babai, P. Frankl, Isomorphisms of Cayley graphs II, Acta Math. Acad. Sci. Hungar. 34 (1979) 177-183.
8. Y.G. Baik, Y.Q. Feng, H.S. Sim, M.Y. Xu, On the normality of Cayley digraphs of abelian groups, preprint, 1995.
9. C.Y. Chao, On the classification of symmetric graphs with a prime number of vertices, Trans. Amer. Math. Soc. 158 (1971) 247-256.
10. Y. Cheng, J. Oxley, On weakly symmetric graphs of order twice a prime, J. Combin. Theory Ser. B 4 (1987) 196-211.
11. X.-G. Fang, A characterization of finite abelian 2-DCI-groups (Chinese), J. Math. (Wuhan) 8 (1988) 315-317.
12. X.-G. Fang, Abelian 3-DCI-groups of even order, Ars Combin. 32 (1991) 263-267.
13. X.-G. Fang, M.-Y. Xu, Abelian 3-DCI-groups of odd order, Ars Combin. 28 (1989) 247-251.
14. X.-G. Fang, Ming-Yao Xu, On isomorphisms of Cayley graphs of small valency, Algebra Colloq. 1 (1994) 67-76.
15. 4, preprint, 1995.
16. Y.-Q. Feng, M.-Y. Xu, A note on Cayley digraph isomorphisms of abelian groups, Austral. J. Combin. 15 (1997) 87-90.
17. C.D. Godsil, GRRs for non-solvable groups, Colloq. Math. Soc. Jannos Bolyai 25 (1978) 221-239.
18. C.D. Godsil, On the full automorphism group of a graph, Combinatorica 1 (1981) 243-256.
19. C.D. Godsil, On Cayley graph isomorphisms, Ars Combin. 15 (1983) 231-246.
20. F. Gross, Conjugacy of odd order Hall subgroups, Bull. London Math. Soc. 19 (1987) 311-319.
21. Q. Huang, Cayley graphs and infinite circulant graphs, Ph.D. Thesis, Xinjiang University, 1995.
22. Q. Huang, J. Meng, Isomorphisms of circulant digraphs, Appl. Math.-JCU 9B (1994) 405-409.
23. Q. Huang, J. Meng, Automorphism groups of Cayley digraphs, in: Combinatorics, Graph Theory, Algorithms and Applications, Y. Alavi, D.R. Lick, Jiuqiang Liu (Eds.), World Scientific, Singapore, 1994, pp. 77-81.
24. Q. Huang, J. Meng, On the isomorphisms and automorphism groups of circulants, Graphs Combin. 12 (1996) 179-187.
25. C.-H. Li, Isomorphisms of connected Cayley di-graphs, preprint, 1995.
26. X.-H. Li, On isomorphisms of Cayley digraphs of simple groups, preprint, 1995.
27. 2, in preparation.
28. J.-X. Meng, M.-Y. Xu, Weakly 5-CI abelian groups, in: Ku Tung-Hsin (Ed.), Combinatorics and Graph Theory '95, vol. 1, SSICC'95, Proc. of the Summer School and Internat. Conf. on Combinatorics; World Scientific, Singapore, pp. 301-307.
29. J.-X. Meng, M.-Y. Xu, Weakly 3-DCI abelian groups, Austral. J. Combin. 13 (1996) 49-60.
30. J.-X. Meng, M.-Y. Xu, Weakly m-DCI abelian groups, submitted.
31. P.P. Pàlfy, Isomorphism problem for relational structures with a cyclic automorphism, Europ. J. Combin. . 8 (1987) 35-43.
32. C.E. Praeger, R.-J. Wang, M.-Y. Xu, Symmetric graphs of order a product of two distinct primes, J. Combin. Theory Ser. B 58 (1993) 299-318.
33. C.E. Praeger, M.-Y. Xu, Vertex primitive graphs of order a product of two distinct primes, J. Combin. Theory Ser. B 59 (1993) 245-266.
34. R.-J. Wang, 1/2-transitive graphs of order a product of two distinct primes, Commun. Algebra 22 (1994) 915-927.
35. C.-Q. Wang, D.-J. Wang, M.-Y. Xu, On normal Cayley graphs of finite groups, submitted.
36. R.-J. Wang, M.-Y. Xu, A classification of symmetric graphs of order 3p, J. Combin. Theory Ser. B 58 (1993) 197-216.
37. 3, Adv. Math. (China) 17 (1988) 427-428.
38. 3, preprint, 1988.
39. M.-Y. Xu, Some work on vertex-transitive graphs by Chinese mathematicians, in: Group Theory in China, Science Press/Kluwer Academic Publishers, Beijing/New York, 1996, pp. 224-254.