Quantum state transfer on integral oriented circulant graphs

Abstract: An oriented circulant graph is called integral if all eigenvalues of its Hermitian adjacency matrix are integers. The main purpose of this paper is to investigate the existence of perfect state transfer ($\PST$ for short) and multiple state transfer ($\MST$ for short) on integral oriented circulant graphs. Specifically, a characterization of $\PST$ (or $\MST$) on integral oriented circulant graphs is provided. As an application, we also obtain a closed-form expression for the number of integral oriented circulant graphs with fixed order having $\PST$ (or $\MST$).