# Write formula in MSO expressing that graph is grid (many variants)

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 only at 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 ?