Perfect state transfer on weighted bi-Cayley graphs over abelian groups

Abstract

The study of perfect state transfer on graphs has attracted extensive attention because of its application in quantum information and computation. This paper establishes necessary and sufficient conditions for a weighted bi-Cayley graph having perfect state transfer over any given finite abelian group. As special cases of weighted bi-Cayley graphs, the results in this paper can apply to examine weighted Cayley graphs having perfect state transfer over dihedral groups, generalized dihedral groups, semi-dihedral groups and dicyclic groups.