Consider $n=3$, we have $9$ vertices in the plane. The vertices are:

$(1,1),\quad(1,2),\quad (1,3), \quad (2,1),\quad (2,2),\quad (2,3),\quad (3,1),\quad (3,2),\quad (3,3)$

So, the corresponding graph will be:

The cost of the edge between the vertices $(2,3)$ and $(2,2)=1$ and the cost of the edge between the vertices $(2,2)$ and $(2,1)=1$.

M**inimum spanning tree:**

(One of the possibilities)

There is no problem with minimum spanning tree. We have $n^{2}$ vertices so, the minimum spanning tree contains $n^{2}- 1$ edges of cost $1$. So, the cost of the minimum spanning tree is $n^{2}-1$.

**Maximum spanning tree:**

In this maximum spanning tree of $n^{2}$ $-$$ 1$ edges $n^{2}$ $-$$ 2$ edges is of cost ${\sqrt{2}}$ and $1$ edge is of cost $1$.

So, the answer is ${\sqrt{2}}$ $\left ( n{^{2}}-2 \right )+1$.

This pattern continues for high values of $n.$

For $n=4$, the maximum spanning tree is:

(one of possibilities)

For $n=4,16$ vertices are there and the maximum spanning tree requires $15$ edges. Out of $15$ edges, $14$ edges are of cost ${\sqrt{2}}$ and $1$ edge is of cost $1$. Thus satisfying the formula ${\sqrt{2}}$ $\left ( n{^{2}}-2 \right )$ $+1$.

The cost of Minimum spanning tree is: $n^{2}-1$.

The cost of Maximum spanning tree is: $\left ( n^{2}-2 \right )\sqrt{2}+1$.