Classifying Arc-Transitive Circulants
István Kovács
DOI: 10.1023/B:JACO.0000048519.27295.3b
Abstract
A circulant is a Cayley digraph over a finite cyclic group. The classification of arc-transitive circulants is shown. The result follows from earlier descriptions of Schur rings over cyclic groups.
Pages: 353–358
Keywords: arc-transitive circulants; Schur rings; cyclic group
Full Text: PDF
References
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2. S. Evdokimov and I. Ponomarenko, “Characterization of cyclotomic schemes on a finite field and normal Schur rings over a cyclic group,” Algebra and Analysis 14(2) (2002), 11-55.
3. C. Godsil, “On the full automorphism group of a graph,” Combinatorica 1 (1981), 243-256.
4. K.H. Leung and S.L. Ma, “The structure of Schur rings over cyclic groups,” J. Pure Appl. Algebra 66 (1990), 287-302.
5. C.H. Li, “On isomorphisms of finite Cayley graphs-a survey,” Discrete Mathematics 256 (2002), 301-334.
6. C.H. Li, “Permutation groups with a cyclic regular subgroup and arc-transitive circulants,” submitted to J. of Combinatorics (2003).
7. C. Li, D. Maru\check si\check c, and J. Morris, “Classifying arc-transitive circulants of square-free order,” J. of Algebraic Combinatorics 14 (2001), 145-151.
8. M. Muzychuk, “On the structure of basic sets of Schur rings over cyclic groups,” J. of Algebra 169(2) (1994), 655-678.
9. M. Muzychuk, M. Klin, and R. P\ddot oschel, “The isomorphism problem for circulant graphs via Schur ring theory,” DIMACS Series in Discrete Mathematics and Theoretical Computer Science 56 (2001), 241-264.
10. H. Wielandt, Finite Permutation Groups, Academic Press, New York, 1964.