## Abstract

The minimum neighborhood and combinatorial property are two important indicators of fault tolerance of a multiprocessor system. Given a graph G , θ _{G} (q) is the minimum number of vertices adjacent to a set of q vertices of G (1 ≤|V(G)| ). It is meant to determine θ _{G} (q), the minimum neighborhood problem (MNP). In this paper, we obtain θ _{AGn} (q) for an independent set with size q in an n -dimensional alternating group graph AG _{n} , a well-known interconnection network for multiprocessor systems. We first propose some combinatorial properties of AG _{n} . Then, we study the MNP for an independent set of two vertices and obtain that θ _{AGn} (2)=4n-10. Next, we prove that θ _{AGn} (3)=6n-16. Finally, we propose that θ _{AGn} (4)=8n-24.

Original language | English |
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Article number | 8629905 |

Pages (from-to) | 17299-17311 |

Number of pages | 13 |

Journal | IEEE Access |

Volume | 7 |

DOIs | |

State | Published - 2019 |

## Keywords

- Minimum neighborhood
- alternating group graphs
- combinatorial property
- fault tolerance
- independent set