{2,3}-Extraconnectivities of hypercube-like networks
{2,3}-Extraconnectivities of hypercube-like networks
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DOI：
10.1016/j.jcss.2013.01.013
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
Nai-Wen Chang;S. Hsieh
中科院分区：
文献类型：
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作者：
Nai-Wen Chang;S. Hsieh
如果G−X不连通，则顶点X的子集称为割集。一个割集X称为Rg-割集，如果G-X的每个分支至少有g+1个顶点。若G至少有一个Rg-割集，则G的g-外连通度定义为G在所有Rg-割集上的最小基数.在本文中，我们首先证明了一个n维超立方体网络的2-外连通性是3 n −5，其中n ≠ 5。这改进了之前最著名的结果，即n维超立方体网络的2-外连通度是3 n −5（n = 8）。我们进一步证明了一个n维类超立方体网络的3-外连通度是4 n −9（n = 6）。基于上述结果，可以有效地确定超立方体、扭立方体、交叉立方体、Möbius立方体、局部扭立方体、广义扭立方体、递归循环和Mcube等互连网络的2-外连通性和3-外连通性.
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.