The domination number of exchanged hypercubes

Exchanged hypercubes (Loh et al., 2005 [13]) are spanning subgraphs of hypercubes with about one half of their edges but still with many desirable properties of hypercubes. Lower and upper bounds on the domination number of exchanged hypercubes are proved which in particular imply that gamma(EH(2, t)) = 2(t+1) holds for any t >= 2. Using Hamming codes we also prove that gamma (EH(s, 2(k) -1)) <= (2(s) - 2(k))gamma(Q(2k-1)) + (gamma(Q(s)(-)) + 1) holds for s >= k >= 3. (C) 2013 Elsevier B.V. All rights reserved.