I'm working on a problem involving graph traversal algorithms, specifically Breadth-First Search (BFS) and Depth-First Search (DFS). I'm a beginner in these concepts, so I would appreciate a simple and easy-to-understand solution.

In the attached image, you'll find a graph G. Here are the tasks:

(a) Perform BFS starting at vertex A, labeling each edge as either a discovery or cross edge.

(b) Perform DFS starting at vertex A, labeling each edge as either a discovery or back edge.

Note: When multiple vertices are available for traversal, select the vertex whose label occurs earliest in the alphabet.

Could you provide a step-by-step walkthrough of these traversals, keeping the explanation as straightforward as possible for a beginner?

A A B B G G D E D E F F