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I would like to define a graph where I want my vertices set to $\mathbb{F}_5^2$. I won't define there is an edge between $(A_0,B_0)$ and $(A,B)$ if $A\neq A_0$ and $F_{B-B_0}(A,B))=0$ Where $F_{A,B}(X)=X^3+AX+B$. Any help or reference is appreciated.