Adjacency Lists:

10 -> 4 -> 3
6 -> 2
7 -> 1 -> 4
8 -> 4 -> 5
1 -> 7
3 -> 10 -> 9
9 -> 3 -> 5 -> 2
5 -> 8 -> 9
4 -> 7 -> 10 -> 8
2 -> 9 -> 6

The breadth-first solution:

 F |  |   
 W |  |   
 G |  |   
 C |  |   


   |  | F 
 W |  |   
   |  | G 
 C |  |   


 F |  |   
 W |  |   
   |  | G 
 C |  |   


   |  | F 
   |  | W 
   |  | G 
 C |  |   


 F |  |   
   |  | W 
 G |  |   
 C |  |   


   |  | F 
   |  | W 
 G |  |   
   |  | C 


 F |  |   
   |  | W 
 G |  |   
   |  | C 


The depth-first solution:

 F |  |   
 W |  |   
 G |  |   
 C |  |   


   |  | F 
 W |  |   
   |  | G 
 C |  |   


 F |  |   
 W |  |   
   |  | G 
 C |  |   


   |  | F 
 W |  |   
   |  | G 
   |  | C 


 F |  |   
 W |  |   
 G |  |   
   |  | C 


   |  | F 
   |  | W 
 G |  |   
   |  | C 


 F |  |   
   |  | W 
 G |  |   
   |  | C