Bounding the size of the subgraph induced by m vertices and extra edge-connectivity of hypercubes

In this note, we show that a subgraph induced by m (denote m by Sigma(s)(i=0) 2(ti), t(0) = [log(2) m] and ti = [log(2) (m - Sigma(i-1)(r=0) 2(tr))] for i >= 1) vertices of an n-dimensional hypercube has at most Sigma(s)(i=0) t(i)2(t-1) + Sigma(s)(i=0) i . 2(ti) edges. As an application, we determine the m-extra edge-connectivity of hypercubes for m <= 2([n/2]). (C) 2013 Elsevier B.V. All rights reserved.