As a generalization of the traditional connectivity, the g-component edge connectivity c{\lambda}g(G) of a non-complete graph G is the minimum number of edges to be deleted from the graph G such that the resulting graph has at least g components. Hypercube-like networks (HL-networks for short) are obtained by manipulating some pairs of edges in hypercubes, which contain several famous interconnection networks such as twisted cubes, Mobius cubes, crossed cubes, locally twisted cubes. In this paper, we determine the (g + 1)-component edge connectivity of the n-dimensional HL-networks.
翻译:作为传统连通的概括,非完整的图表G的g-成分边缘连通c=lambda}g(G)是将从图形G中删除的最低边数,因此所产生的图形至少有 g 组件。超立方体类网络(短的HL-网络)是通过在超立方体中操纵一些边缘获得的,超立方体中包含若干著名的连通网络,如扭曲立方体、莫比乌斯立方体、跨立方体、本地扭曲立方体。在本文中,我们确定了(g+1)n-二维HL网络的(g+1)组成边缘连通性。