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In monadic second order logic write formula in MSO such that it express graph that is grid: $(\text{rows}\times\text{columns})$. Keep in mind that MSO mean in my case formulas in MSO can quantify over sets

onlyat front of formula.

(a) $(n\times n)$

(b) $(n\times n^2)$

(c) $(n\times 2^n)$

At start I am going to try solve (a):

I am not sure If I can properly and elegant express this grid:

- there exists excatly $n^2$ nodes
- exactly $n^2 -4n + 4$ has degree $4$
- exactly 4 of them has has degree $2$
- exactly $4(n-2)$ of them has degree $3$
- grid is connected

Can you help me, please ?

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