$6.$ Consider the following weighted graph G$($V$,$ E$)$ presented by the adjacency matrix.

G $=$

A B C D E F

A $040\backslash$infty $\backslash$infty $721$

B $400512\backslash$infty $11$

C $\backslash$infty $5010\backslash$infty $\backslash$infty

D $\backslash$infty $121001814$

E $7\backslash$infty $\backslash$infty $18033$

F $2111\backslash$infty $14330$

$(1)(6\%)$ Please find the vertex sequence derived by DFS and BFS respectively. Note that we assume that node A is the root. You should draw the graph.

$(2)(4\%)$ Please apply Kruskal$$s algorithm to drive the minimum cost spanning tree. Note that you must show your actions step by step.