A compact domain in R n is a spectral set if there is some subset of R n such that fexp(2ih; xi) : 2 g when restricted to gives an orthogonal basis of L 2 ((). The set is called a spectrum for. We give a criterion for being a spectrum of a given set in terms of tiling Fourier space by translates of a suitable auxiliary set D. We apply this criterion to classify all spectra for the n-cube by sho...

In this paper, by combining with the network structures of the twisted n cube and the crossed cube, the counterchanged crossed cube network is proposed, a rigorous recursive definition is made, and the network topology structure graph is offered. Basing on the definition of the counterchanged crossed cube, this paper also analyzes the basic properties of the network, proves that the network is ...