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    Normality of one-matching semi-Cayley graphs over finite abelian groups with maximum degree three

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    A graph Γ\Gamma is said to be a semi-Cayley graph over a group GG if it admits GG as a semiregular automorphism group with two orbits of equal size. We say that Γ\Gamma is normal if GG is a normal subgroup of Aut(Γ){\rm Aut}(\Gamma). We prove that every connected intransitive one-matching semi-Cayley graph, with maximum degree three, over a finite abelian group is normal and characterize all such non-normal graphs.Comment: 10 page
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