Abstract
Recently, there are extensive studies on perfect state transfer on graphs due to their significant applications in quantum information processing and quantum computations. However, most of the graphs previously investigated are abelian Cayley graphs. In this paper, we study perfect state transfer on Cayley graphs over dihedral groups. Using the representations of the dihedral group , we present some necessary and sufficient conditions for the Cayley graph to have a perfect state transfer between two distinct vertices for some connection set S. Based on these conditions, we show that cannot have PST if n is odd and S is conjugation-closed. For some even integers n, it is possible for to have PST, some concrete constructions are provided.
COMMUNICATED BY:
Acknowledgments
The authors would like to express their grateful thankfulness to the referee for their valuable comments and suggestions. X. Cao would like to thank the Institute of Mathematics, Academia Sinica for the financial support during his visiting.
Disclosure statement
No potential conflict of interest was reported by the authors.