### 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 |
---|---|

Article number | 8629905 |

Pages (from-to) | 17299-17311 |

Number of pages | 13 |

Journal | IEEE Access |

Volume | 7 |

DOIs | |

State | Published - 1 Jan 2019 |

### Fingerprint

### Keywords

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

### Cite this

*IEEE Access*,

*7*, 17299-17311. [8629905]. https://doi.org/10.1109/ACCESS.2019.2896101

}

*IEEE Access*, vol. 7, 8629905, pp. 17299-17311. https://doi.org/10.1109/ACCESS.2019.2896101

**Minimum Neighborhood of Alternating Group Graphs.** / Huang, Yanze; Lin, Limei; Wang, Dajin; Xu, Li.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Minimum Neighborhood of Alternating Group Graphs

AU - Huang, Yanze

AU - Lin, Limei

AU - Wang, Dajin

AU - Xu, Li

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Minimum neighborhood

KW - alternating group graphs

KW - combinatorial property

KW - fault tolerance

KW - independent set

UR - http://www.scopus.com/inward/record.url?scp=85061699184&partnerID=8YFLogxK

U2 - 10.1109/ACCESS.2019.2896101

DO - 10.1109/ACCESS.2019.2896101

M3 - Article

AN - SCOPUS:85061699184

VL - 7

SP - 17299

EP - 17311

JO - IEEE Access

JF - IEEE Access

SN - 2169-3536

M1 - 8629905

ER -