Fractional revival on Cayley graphs over abelian groups

In this paper, we investigate the existence of fractional revival on Cayley graphs over finite abelian groups. We give a necessary and sufficient condition for Cayley graphs over finite abelian groups to have fractional revival. As applications, the existence of fractional revival on circulant graphs and cubelike graphs are characterized

A Characterization of State Transfer on Double Subdivided Stars

A subdivided star $SK_{1,l}$ is obtained by identifying exactly one pendant vertex from $l$ copies of the path $P_3.$ This study is on the existence of quantum state transfer on double subdivided star $T_{l,m}$ which is a pair of subdivided stars $SK_{1,l}$ and $SK_{1,m}$ joined by an edge to the respective coalescence vertices. Using the Galois group of the characteristic polynomial of $T_{l,m},$ we analyze the linear independence of its eigenvalues which uncovers no perfect state transfer in double subdivided stars when considering the adjacency matrix as the Hamiltonian of corresponding quantum system. Then we establish a complete characterization on double subdivided stars exhibiting pretty good state transfer