Functional graph trees for circulants with linear Boolean functions at the vertices

The functional graph of a discrete dynamic system being a model of regulatory gene network circuit is defined as the graph of the transformation $A_{f,2}:F_{2}^{n}\rightarrow F_{2}^{n}$ where $A_{f,2}(v_0,v_1,\ldots,v_{n-1}) = (u_0,u_1,\ldots,u_{n-1})$, $u_i=v_{i-1}+v_i+v_{i+1}$, $i=0,1,\ldots,n-1$, $v_{-1}=v_{n-1}$, $v_n=v_0$. The structure of this graph is completely described.