More Circulant Graphs exhibiting Pretty Good State Transfer

The transition matrix of a graph $G$ corresponding to the adjacency matrix $A$ is defined by $H(t):=\exp (-itA),$ where $t\in \mathbb{R}$. The graph is said to exhibit pretty good state transfer between a pair of vertices $u$ and $v$ if there exists a sequence $\left\{t_k\right\}$ of real numbers such that $\lim\limits_{k\rightarrow\infty} H(t_k) {\bf e}_u=\gamma {\bf e}_v$,where$\gamma$ is a complex number of unit modulus. We classify some circulant graphs exhibiting or not exhibiting pretty good state transfer. This generalize several pre-existing results on circulant graphs admitting pretty good state transfer.