Abstract:In this paper, we show that a Cayley graph for an abelian group has an independent perfect domination set if and only if it is a covering graph of a complete graph. As an application, we show that the hypercube Q n has an independent perfect domination set if and only if Q n is a regular covering of the complete graph K n 1 if and only if n 2 m À 1 for some natural number m.

4 J. MAGN. RESON. IMAGING 2017;45:1394-1406.

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We show that nontrivial classical pretzel knots L (p,q,r) are hyperbolic with eight exceptions which are torus knots. We find Conway polynomials of n-pretzel links using a new computation tree. As applications, we compute the genera of n-pretzel links using these polynomials and find the basket number of pretzel links by showing that the genus and the canonical genus of a pretzel link are the same.