More circulant graphs exhibiting pretty good state transfer

Abstract

The transition matrix of a graph G corresponding to the adjacency matrix A is defined by H(t)≔exp−itA, 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 tk of real numbers such that limk→∞H(tk)eu=γev, 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.