### Abstract

A subset of vertices X is said to be a cutset if G-X is not connected. A cutset X is called an ^{Rg}-cutset if every component of G-X has at least g+1 vertices. If G has at least one ^{Rg}-cutset, the g-extraconnectivity of G is then defined as the minimum cardinality over all ^{Rg}-cutsets of G. In this paper, we first show that the 2-extraconnectivity of an n-dimensional hypercube-like network is 3n-5 for n≥5. This improves on the previously best known result, which showed that the 2-extraconnectivity of an n-dimensional hypercube-like network is 3n-5 for n≥8. We further demonstrate that the 3-extraconnectivity of an n-dimensional hypercube-like network is 4n-9 for n≥6. Based on the above results, the 2-extraconnectivity and 3-extraconnectivity of several interconnection networks, including hypercubes, twisted cubes, crossed cubes, Möbius cubes, locally twisted cubes, generalized twisted cubes, recursive circulants, and Mcubes, can be determined efficiently.

Original language | English |
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Pages (from-to) | 669-688 |

Number of pages | 20 |

Journal | Journal of Computer and System Sciences |

Volume | 79 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2013 Aug 1 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics