The domination number of exchanged hypercubes

Authors:
Sandi Klavar;Meijie Ma
Affiliations:
Faculty of Mathematics and Physics, University of Ljubljana, Slovenia and Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia and Institute of Mathematics, Physics and Mec ...;Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China
Venue:
Information Processing Letters
Year:
2014

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Abstract

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 @c(EH(2,t))=2^t^+^1 holds for any t=2. Using Hamming codes we also prove that @c(EH(s,2^k-1))==k=3.