### Abstract

Given a class C of Cayley graphs, and given an edge-colored graph G of n vertices and m edges, we are interested in the problem of checking whether there exists an isomorphism 0 preserving the colors such that G is isomorphic by 0 toagraph in C colored by the elements of its generating set. In this paper, we give an 0(m log n)-time algorithm to check whether G is color-isomorphic to a Cayley graph, improving a previous 0(n4'752 log n) algorithm. In the case where C is the class of the Cayley graphs defined on Abelian groups, we give an optimal 0(m)-time algorithm. This algorithm can be extended to check color-isomorphism with Cayley graphs on Abelian groups of given rank. Finally, we propose an optimal 0(m)-time algorithm that tests color-isomorphism between two Cayley graphs on Z„, i.e., between two circulant graphs. This latter algorithm is extended to an optimal 0(n)-time algorithm that tests color-isomorphism between two Abelian Cayley graphs of bounded degree.

Original language | English |
---|---|

Pages (from-to) | 76-87 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 1879 |

Publication status | Published - 2000 |

## Fingerprint Dive into the research topics of 'On recognizing cayley graphs'. Together they form a unique fingerprint.

## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*1879*, 76-87.