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

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

### Cite this

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*Journal of Computer and System Sciences*, vol. 79, no. 5, pp. 669-688. https://doi.org/10.1016/j.jcss.2013.01.013

**{2, 3} -Extraconnectivities of hypercube-like networks.** / Chang, Nai Wen; Hsieh, Sun Yuan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - {2, 3} -Extraconnectivities of hypercube-like networks

AU - Chang, Nai Wen

AU - Hsieh, Sun Yuan

PY - 2013/8/1

Y1 - 2013/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84875232028&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875232028&partnerID=8YFLogxK

U2 - 10.1016/j.jcss.2013.01.013

DO - 10.1016/j.jcss.2013.01.013

M3 - Article

AN - SCOPUS:84875232028

VL - 79

SP - 669

EP - 688

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

SN - 0022-0000

IS - 5

ER -