## Abstract

A circulant graph G of order n is a Cayley graph over the cyclic group Z_{n}. Equivalently, G is circulant iff its vertices can be ordered such that the corresponding adjacency matrix becomes a circulant matrix. To each circulant graph we may associate a coherent configuration A and, in particular, a Schur ring S isomorphic to A. A can be associated without knowing G to be circulant. If n is prime, then by investigating the structure of A either we are able to find an appropriate ordering of the vertices proving that G is circulant or we are able to prove that a certain necessary condition for G being circulant is violated. The algorithm we propose in this paper is a recognition algorithm for cyclic association schemes. It runs in time polynomial in n.

Original language | English |
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Article number | R25 |

Number of pages | 28 |

Journal | Electronic Journal of Combinatorics |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 1998 |

Externally published | Yes |

## Keywords

- Circulant graph
- Cyclic association scheme
- Recognition algorithm