On Cayley Graphs of Abelian Groups
Cai Heng Li
DOI: 10.1023/A:1008650130591
Abstract
Let G be a finite Abelian group and $Cay(G, S)$ the Cayley (di)-graph of G with respect to S, and let A = Aut $Cay(G, S)$ and A1 the stabilizer of 1 in A. In this paper, we first prove that if A1 is unfaithful on S then S contains a coset of some nontrivial subgroup of G, and then characterize $Cay(G, S)$ if AS contains the alternating
Pages: 205–215
Keywords: Cayley graph; isomorphism; CI-subset; $m$-DCI group
Full Text: PDF
References
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2. L. Babai and P. Frankl, “Isomorphisms of Cayley graphs I,” Colloq. Math. Soc. J. Bolyai 18 (Combinatorics, Keszthely, 1976), North-Holland, Amsterdam, 1978, 35-52.
3. C. Delorme, O. Favaron, and M. Mahéo, “Isomorphisms of Cayley multigraphs of degree 4 on finite abelian groups,” Europ. J. Combin. 13 (1992), 59-61.
4. E. Dobson, “Isomorphism problem for Cayley graph of Z3p,” Disc. Math. 147 (1995), 87-94.
5. C.D. Godsil, “On the full automorphism group of a graph,” Combinatorica 1 (1981), 243-256.
6. C.D. Godsil, “On Cayley graph isomorphisms,” Ars Combin. 15 (1983), 231-146.
7. F. Gross, “2-automorphic 2-groups,” J. Algebra 40 (1976), 348-353.
8. C.H. Li, “On isomorphisms of connected Cayley graphs,” Disc. Math. 178 (1998), 109-122.
9. C.H. Li and C.E. Praeger, “On the isomorphism problem for finite Cayley graphs of bounded valency,” preprint, 1997.
10. C.H. Li, C.E. Praeger, and M.Y. Xu, “Isomorphisms of finite Cayley digraphs of bounded valency,” J. Combin. Theory, series, to appear.
11. L.A. Nowitz, “A non-Cayley-invariant Cayley graph of the elementary Abelian group of order 64,” Disc. Math. 110 (1992), 223-228.
12. P.P. Pálfy, “Isomorphism problem for relational structures with a cyclic automorphism,” Europ. J. Combin. 8 (1987), 35-43.
13. E.E. Shult, “On finite automorphic algebras,” Illinois J. Math. 13 (1969), 625-653.
14. M. Suzuki, Groups Theory II, Spring-Verlag, New York, 1982.
15. H. Wielandt, Finite Permutation Groups, Academic Press, New York, 1964.
16. M.Y. Xu, “On isomorphisms of Cayley digraphs and graphs of groups of order p3,” preprint.