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- S is a subset of
then is a CI-digraph.
The conjecture was then fully proven by Muzychuk, Klin, and Poschel in 2001 by using Schur algebra, and simultaneously by Dobson and Morris in 2002 by using the Classification of finite simple groups.
- *S. Toida: "A note on Adam's conjecture", J. of Combinatorial Theory (B), pp. 239–246, October–December 1977
- *Klin, M.H. and R. Poschel: The Konig problem, the isomorphism problem for cyclic graphs and the method of Schur rings, Algebraic methods in graph theory, Vol. I, II., Szeged, 1978, pp. 405–434.
- *Golfand, J.J., N.L. Najmark and R. Poschel: The structure of S-rings over Z2m , preprint (1984).
- Klin, M.H., M. Muzychuk and R. Poschel: The isomorphism problem for circulant graphs via Schur ring theory, Codes and Association Schemes, American Math. Society, 2001.
- *E. Dobson, J. Morris: TOIDA’S CONJECTURE IS TRUE, PhD Thesis, 2002.
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