Edge neighbor connectivity of Cartesian product graph G×K2

摘要

Let G be a k-regular graph with girth at least 4, connectivity k, and restricted connectivity 2k-2. We prove in this paper that the edge neighbor connectivity of G×K2 is k. As a consequence, the edge neighbor connectivity of n-dimensional hypercube is n-1. Furthermore, we prove that the edge neighbor connectivity of Kn×K2 is ⌈n/2⌉.