### Abstract

The alternating group graph, which belongs to the class of Cayley graphs, is one of the most versatile interconnection networks for parallel and distributed computing. Cycle embedding is an important issue in evaluating the efficiency of interconnection networks. In this paper, we show that an n-dimensional alternating group graph AG_{n} has the following results, where F is the set of faulty vertices and/or faulty edges in AG_{n} : (1) For n ≥ 4, AG_{n}-F is edge 4-pancyclic if |F| ≤ n − 4; and (2) For n ≥ 3, AG_{n}-F is vertex-pancyclic if |F| ≤ n − 3. All the results are optimal with respect to the number of faulty elements tolerated, and they are improvements over the cycle embedding properties of alternating group graphs proposed previously in several articles.

Original language | English |
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Title of host publication | Advanced Technologies, Embedded and Multimedia for Human-Centric Computing, HumanCom and EMC 2013 |

Publisher | Springer Verlag |

Number of pages | 1 |

ISBN (Print) | 9789400772618 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

Externally published | Yes |

Event | Advanced Technologies, Embedded and Multimedia for Human-Centric Computing, HumanCom and EMC 2013 - , Taiwan Duration: 2013 Aug 23 → 2013 Aug 25 |

### Publication series

Name | Lecture Notes in Electrical Engineering |
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Volume | 260 |

ISSN (Print) | 1876-1100 |

ISSN (Electronic) | 1876-1119 |

### Conference

Conference | Advanced Technologies, Embedded and Multimedia for Human-Centric Computing, HumanCom and EMC 2013 |
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Country | Taiwan |

Period | 13/8/23 → 13/8/25 |

### Keywords

- Alternating group graph
- Cayley graph
- Cycle embedding
- Fault-tolerant
- Interconnection network
- Pancyclicity

### ASJC Scopus subject areas

- Industrial and Manufacturing Engineering

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## Cite this

*Advanced Technologies, Embedded and Multimedia for Human-Centric Computing, HumanCom and EMC 2013*(Lecture Notes in Electrical Engineering; Vol. 260). Springer Verlag. https://doi.org/10.1007/978-94-007-7262-5_145