### Abstract

Several relations on graphs, including primitive equivalence, explosion equivalence and strong shift equivalence, are examined and shown to preserve either the graph groupoid, a construction of Kumjian, Pask, Raeburn, and Renault, or the groupoid of a pointed version of the graph. Thus these relations preserve either the isomorphism class or the Morita equivalence class of the graph C*-algebra, as defined by Kumjian, Pask, and Raeburn.

Original language | English (US) |
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Pages (from-to) | 209-229 |

Number of pages | 21 |

Journal | Journal of Operator Theory |

Volume | 45 |

Issue number | 1 |

State | Published - Jan 1 2001 |

Externally published | Yes |

### Keywords

- Explosion
- Graph C*-algebra
- Graph groupoid
- Primitive equivalence
- Strong shift equivalence

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Drinen, D., & Sieben, N. (2001). C*-equivalences of graphs.

*Journal of Operator Theory*,*45*(1), 209-229.