Perfect state transfer on semi-Cayley graphs over abelian groups

TL;DR

This paper characterizes the conditions under which perfect state transfer occurs in semi-Cayley graphs over abelian groups, extending previous results and providing new classifications for related Cayley graphs.

Contribution

It provides a new characterization of semi-Cayley graphs over abelian groups with perfect state transfer, improving earlier classifications for various group-based Cayley graphs.

Findings

Characterization of semi-Cayley graphs over abelian groups with PST

Extended results for Cayley graphs over groups with abelian subgroups of index 2

Determined PST conditions for Cayley graphs over generalized dihedral and dicyclic groups

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.