ABSTRACT

In this paper, we consider the problem on the existence of perfect state transfer (PST for short) on semi-Cayley graphs over abelian groups (which are not necessarily regular), i.e. on the graphs having semiregular and abelian subgroups of automorphisms with two orbits of equal size. We stablish a characterization of semi-Cayley graphs over abelian groups having PST. As a result, we give a characterization of Cayley graphs over groups with an abelian subgroup of index 2 having PST, which improves the earlier results on Cayley graphs over abelian groups, dihedral groups and dicyclic group and determines Cayley graphs over generalized dihedral groups and generalized dicyclic groups having PST.

摘要

在本文中，我们考虑阿贝尔群（不一定是正则）上的半凯莱图上完美状态转移（简称PST）的存在性问题，即在具有两个轨道的自同构的半正则和阿贝尔子群的图上大小相等。我们建立了具有 PST 的阿贝尔群上的半凯莱图的表征。因此，我们给出了具有 PST 的索引为 2 的阿贝尔子群的群上凯莱图的表征，这改进了阿贝尔群、二面体群和双环群上凯莱图的早期结果，并确定了广义二面体群和广义凯莱图具有PST的双环基团。