Bitcoin is an example of an application of blockchain that uses peer$-$to$-$peer transactions

without the need for a trusted intermediary.

$($i$)$ In the context of partition attacks on Bitcoin, what is a vertex cut?

$($ii$)$ Does a complete graph have a vertex cut?

$($iii$)$ Give the minimum vertex cut for the graph, G$,$ in Fig. $4$ and for the graph, F$,$ in

Fig. $5.$

$($iv$)$ Compare the vertex$-$connectivity of graphs G and F$.$ Comment on which type of

graph is more resilient to partition attacks.