More circulant graphs exhibiting pretty good state transfer

The transition matrix of a graph G corresponding to the adjacency matrix A is defined by H ( t ) ≔ exp − i t A , where t ∈ R . The graph is said to exhibit pretty good state transfer between a pair of vertices u and v if there exists a sequence t k of real numbers such that lim k → ∞ H ( t k ) e u = γ e v , where γ is a complex number of unit modulus. We present a class of circulant graphs admitting pretty good state transfer. Also we find some circulant graphs not exhibiting pretty good state transfer. This generalizes several pre-existing results on circulant graphs admitting pretty good state transfer.