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Let AG(n,Fq)be the n-dimensional affine space over Fq,where Fq is a finite field with q elements.Denote by Γ^(m)the graph induced by m-flats of AG(n,Fq0,For any two adjacent vertices E and Fof Γ^(m),Γ(m)(E)∩Γ^(m)(F)is studied.In particular,sizes of maxima