You are tasked with designing a communication network between several locations on a remote island. The locations are representied as nodes, and the potential communication links between them are represented as edges with weights that indicate the cost of boilding a link Consider the following graph where each edge hass a cost associated with building a communication link $($refer to the diagram provided$)$:

$($a$)$ Apply Prim's algonthm starting from node A$.$ List the edges selected to form the Minimum Spanning Tree $($MST$)$ and the total cost of constructing the netrook

$($b$)$ Suppose you need to build this netroote starting from node E instead. Does this result in a different MST$?$ Explain rwhy or why not and provide the resulting edges and total cost. $\backslash (\backslash$quad $4+3\backslash )$ Marks$]$