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We study perfect state transfer in Grover walks, which are typicaldiscrete-time quantum walk models. In particular, we focus on states associatedto vertices of a graph. We call such states vertex type states. Perfect statetransfer between vertex type states can be studied via Chebyshev polynomials.We derive a necessary condition on eigenvalues of a graph for perfect statetransfer between vertex type states to occur. In addition, we perfectlydetermine the complete multipartite graphs whose partite sets are the same sizeon which perfect state transfer occurs between vertex type states, togetherwith the time.

Perfect state transfer in Grover walks between states associated to vertices of a graph