Quasi m-Cayley circulants

A graph ▫$Gamma$▫ is called a quasi ▫$m$▫-Cayley graph on a group ▫$G$▫ if there exists a vertex ▫$infty in V(Gamma)$▫ and a subgroup ▫$G$▫ of the vertex stabilizer ▫$text{Aut}(Gamma)_infty$▫ of the vertex ▫$infty$▫ in the full automorphism group ▫$text{Aut}(Gamma)$▫ of ▫$Gamma$▫, such that ▫$G$▫ acts semiregularly on ▫$V(Gamma) setminus {infty}$▫ with ▫$m$▫ orbits. If the vertex ▫$infty$▫ is adjacent to only one orbit of ▫$G$▫ on ▫$V(Gamma) setminus {infty}$▫, then ▫$Gamma$▫ is called a strongly quasi ▫$m$▫-Cayley graph on ▫$G$▫ .In this paper complete classifications of quasi 2-Cayley, quasi 3-Cayley and strongly quasi 4-Cayley connected circulants are given

Weakly distance-regular circulants, I

We classify certain non-symmetric commutative association schemes. As an application, we determine all the weakly distance-regular circulants of one type of arcs by using Schur rings. We also give the classification of primitive weakly distance-regular circulants.Comment: 28 page