$2.$ Given the following adjacency matrix for an un$-$

directed graph.

$($a$)5$ points: Draw the graph with edge weights.

$($b$)10$ points: Give the traversal order of BFS and DFS starting from node

$$s$.$ When enqueue or push unvisited neighbors into queue or stack, follow the

alphabetical order.

$($c$)15$ points: Use Prim$$s algorithm to find a minimum spanning tree $($MST$)$

of the graph. You need to show step by step results and calculate the weight of

the final MST$.$

$($d$)20$ points: Use Dijkstra$$s algorithm to find the shortest path from s to

rest of the nodes in the graph. You need to show step by step results and the

actual shorted paths from s to each node.