The restricted edge-connectivity and restricted connectivity of augmented k-ary n-cubes
The restricted edge-connectivity and restricted connectivity of augmented k-ary n-cubes
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DOI：
10.1080/00207160.2015.1067690
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发表时间：
2016-08
影响因子：
1.8
通讯作者：
Ruizhi Lin;Heping Zhang
中科院分区：
文献类型：
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作者：
Ruizhi Lin;Heping Zhang
Xiang和Steward [Augmented k-ary n-cubes，Inform. Sci. 181（1）（2011），pp. 239-256]。对于连通图G，如果G的边割（点割）S不含孤立点，则称G的边割（点割）S为限制边割（限制点割）。图G的限制边连通度（限制连通度）是图G的所有限制边割（点割）上的最小基数，记为（）。在本文中，我们完全确定了图的限制（边）连通性。准确地说，for ; for，for，for，and，但没有限制的顶点切割。
Augmented k-ary n-cube is proposed as a new interconnection network model by Xiang and Steward [Augmented k-ary n-cubes, Inform. Sci. 181(1) (2011), pp. 239–256]. For a connected graph G, an edge-cut (vertex-cut) S is called a restricted edge-cut (restricted vertex-cut) if G–S contains no isolated vertices. The restricted edge-connectivity (restricted connectivity) of G, denoted by (), is the minimum cardinality over all restricted edge-cuts (vertex-cuts) of G. In this paper, we completely determine the restricted (edge-)connectivity of . Precisely, for ; for , for , for and , but does not have restricted vertex-cut.