$2\mathrm{.}2$ Please enumerate all possible spanning trees $($please draw each of them and calculate the total weight

of each tree$).$

$2\mathrm{.}3$ Is the minimum spanning tree for this graph unique or not? Why?

$2\mathrm{.}4$ If we shuffle the edge weights randomly $($but keep the graph structure with same nodes and edges$),$

would two minimum edges $($which have weight one$)$ be always on the same minimum spanning tree?

Why or why not?

$2\mathrm{.}5$ If we shuffle the edge weights randomly $($but keep the graph structure with same nodes and edges$),$

would the final minimum spanning tree be always unique or not? Under what condition will it be unique?

$2\mathrm{.}6$ Try to design a prompt to obtain the minimum spanning tree from the above given graph and calculate

its total weight. Please include the ChatGPT version, prompt, and screen shot in this question. $($It$\text{'}$s OK if

the prompt is not working perfectly.$)$