Component edge connectivity of hypercube-like networks

Abstract

As a generalization of the traditional connectivity, the g-component edge connectivity cλg(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, Möbius cubes, crossed cubes, locally twisted cubes. In this paper, we determine the (g+1)-component edge connectivity of the n-dimensional HL-networks for g≤2⌈n2⌉, n≥8.