A characterization of state transfer on double subdivided stars

A subdivided star SK1,l is obtained by identifying exactly one pendant vertex from l copies of the path P3. We consider the existence of quantum state transfer on double subdivided star Tl,m which is a pair of subdivided stars SK1,l and SK1,m joined by an edge to the respective coalescence vertices. We provide a complete characterization of double subdivided stars exhibiting pretty good state transfer. Although there is no perfect state transfer on double subdivided stars, we find perfect pair state transfer on Tl,m considering the adjacency matrix as the Hamiltonian of the corresponding quantum system.