Abstract
The isomorphism problem for circulant graphs (Cayley graphs over the cyclic group) which has been open since 1967 is completely solved in this paper. The main result of the paper gives an efficient isomorphism criterion for circulant graphs of arbitrary order. This result also solves an isomorphism problem for colored circulant graphs and some classes of cyclic codes. 2000 Mathematics Subject Classification 05C60 (primary), 05C25, 05E30, 20B25 (secondary).
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