Perfect state transfer in unitary Cayley graphs over local rings

Abstract

In this work, using eigenvalues and eigenvectors of unitary Cayley graphs over finite local rings and elementary linear algebra, we characterize which local rings allowing PST occurring in its unitary Cayley graph. Moreover, we have some developments when $R$ is a product of local rings.

Keywords

• Local rings
• Perfect state transfer
• Unitary Cayley graphs