For smooth convex disks $A$, i.e., convex compact subsets of the plane with non-empty interior, we classify the classes $G^{\text{hom}}(A)$ and $G^{\text{sim}}(A)$ of intersection graphs that can be obtained from homothets and similarities of $A$, respectively. Namely, we prove that $G^{\text{hom}}(A)=G^{\text{hom}}(B)$ if and only if $A$ and $B$ are affine equivalent, and $G^{\text{sim}}(A)=G^{\text{sim}}(B)$ if and only if $A$ and $B$ are similar.

翻译：对于光滑的磁盘元A$,即平面上非空的紧凑子集,我们分别对可以从同质中得来的相交图表类别G ⁇ text{hom}}(A)$和$G{text{sim}}(A)$(A)进行分类。也就是说,我们证明,只有在美元和美元等值的情况下,才能对平面上非空的紧凑子集块美元进行分类,只有美元和美元等值时,才能对相交图类别G ⁇ text{hom}(A)美元和美元等值的类别进行分类,只有A美元和美元相近时,才能对等的类别G{text{sim}{sim}(B)美元进行分类。