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

In this note, we show that a subgraph induced by m (denote m by @?"i"="0^s2^t^"^i, t"0=[log"2m] and t"i=[log"2(m-@?"r"="0^i^-^12^t^"^r)] for i>=1) vertices of an n-dimensional hypercube has at most @?"i"="0^st"i2^t^"^i^-^1+@?"i"="0^si@?2^t^"^i edges. As an application, we determine the m-extra edge-connectivity of hypercubes for m@?2^[^n^2^].

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