$(20$ points$)$ The graph below is represented as undirected graph with labeled nodes $($A$-$H$)$ and edges. Starting from node $A,$ show the sequence of traversal using:

a$.$ Depth$-$First Search $($DFS$)$: Visit as deeply as possible before backtracking, while preferring neighbors in alphabetical order.

b$.$ Breadth$-$First Search $($BFS$)$: Explore all immediate neighbors of the current node before moving deeper, while preferring neighbors in alphabetical order. Include step$-$by$-$step explanations or diagrams for both traversal processes.