4-Valent Cayley Graphs On Finte Abelian Group Z_2ⁿ×Z₂

Let G=Z_m × Z₂（m≥4）be a finite abelian group,Sis a subset of G which is not containing the identity element 1.and S^-1=S,|S|=4,X=Cay（G,S）is the Cayley graph on G with respect to S.In this paper,we shall research the isomorphism of X.and the work goes around the CI-property of X.First,we obtain the condition of X connectivity.Second,we give the element form of Aut（G）and the orbit of S under Aut（G）.Finally,with the help of normality,we prove that every group of G=Z_2ⁿ x Z₂（n≥2）is not a weakly 4-CI-group.At the same time,we give all CI subset and normality subset.On this basis;we study the non-normality group with order 4 on abelian Cayley group.