Pretty Good State Transfer and Fractional Revival in Double Extended Star Graphs

Much research has been done in the realm of quantum walks over networks of qubits. We primarily study a type of graph consisting of a path with two stars connected to the leaves which we call a Double Extended Star. We find that Pretty Good State Transfer can occur in many ways in a Double Extended Star and that Fractional Revival cannot occur in Double Extended Stars except when the length of the path within is one.