Embedded edge connectivity of k-ary n-cubes

The t-embedded edge connectivity eta t(Gn) of an n-dimensional recursive network Gn is the minimum number of edges, if any, whose removal disconnects Gn and each vertex of the resultant network lies in a t-dimensional subnetwork of Gn. The k-ary n-cube is one of the most attractive interconnection networks for parallel computer systems. One of the main results in [15] showed that eta t(Qn3) = 2(n - t)3t for 0 < t < n -1. In this short paper, we generalize the above result and prove that eta t(Qnk) = 2(n - t)kt for 0 < t < n - 1 and odd k > 3.(c) 2022 Elsevier B.V. All rights reserved.