  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.
