Perfect state transfer on Cayley graphs over the dicyclic group

Arezoomand, Majid; Shafiei, Farideh; Ghorbani, Modjtaba

doi:10.1016/j.laa.2021.12.019

Cited by 5 publications

(3 citation statements)

References 17 publications

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“…The purpose of this paper is two-fold: First we present an explicit general method to find the eigenvalues and eigenvectors of the semi-Cayley graphs over abelian groups which facilitates the computations of PST. [18,6,5,3,16] are direct consequences of our results. Also as a result, we investigate the existence of PST on Cayley graphs over generalized dihedral groups and generalized dicyclic groups.…”

Section: Introductionsupporting

confidence: 64%

“…In particular, since if G is an abelian group of even order, a dihedral group, a dicyclic group or a semidihedral group, then it satisfies the above conditions, one can reprove the main results of [3], [5], [6], and [18]. For example, let Γ = Cay(G, T ), where G is an abelian group of order 2n.…”

Section: Remark 2 By Theorem 1 and Corollary 47 One Can Exactly Deter...mentioning

confidence: 99%

“…A characterization of Cayley graphs over abelian group, dihedral groups with conjugateclosed Cayley set, dihedral groups with non-conjugate-closed Cayley set, dicyclic groups and also over semidihedral groups are given in [18,6,5,3,16], respectively. Despite many results on PST on graphs, there are no known constructions of PST on non-abelian Cayley graphs in literature.…”

Section: Introductionmentioning

confidence: 99%

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Perfect state transfer on semi-Cayley graphs over abelian groups

Arezoomand¹

2022

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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.

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