$1.$ Consider the graph in Figure $1.$ Unless otherwise indicated, always visit adjacent nodes in alphabetical order.Figure $1$ Weighted Graph

a$.(10$pts$)$Provide the DFS tree starting at node B$.$

b$.(10$pts$)$Provide the BFS tree starting at node B$.$

c$.(10$pts$)$Provide the DFS tree starting at node F$.$

d$.(10$pts$)$Provide the BFS tree starting at node F$.$

e$.(10$pts$)$Use Kruskal$$s algorithm to derive the MST starting at node K$.$

f$.(10$pts$)$Use Prim$$s algorithm to derive the MST starting at node K

g$.(20$pts$)$Using UCS, determine the shortest path from node A to I. Show the steps, your tables and the resulting path