Depth-First Search is a fundamental algorithm used for traversing and exploring graphs. Below, I’ll outline the steps and provide a Python code implementation for DFS:**Step 1: Introduction to DFS and Graph Representation:** Briefly explain what DFS is and its purpose in graph traversal.

Introduce the concept of a graph and different ways to represent it (e.g., adjacency list, adjacency matrix).

**Step 2: Implementing the Graph:**

Code the graph representation using an adjacency list.

Show how to add vertices and edges to the graph.

```
class Graph:
def __init__(self):
self.graph = {}
def add_vertex(self, vertex):
self.graph[vertex] = []
def add_edge(self, u, v):
self.graph[u].append(v)
self.graph[v].append(u) # For an undirected graph
```

**Step 3: Implementing Depth-First Search (DFS)** Code the DFS algorithm using a recursive approach.

Explain the importance of visited nodes to avoid infinite loops in graphs containing cycles.

```
def dfs_recursive(graph, start, visited):
if start not in visited:
print(start, end=' ')
visited.add(start)
for neighbor in graph[start]:
dfs_recursive(graph, neighbor, visited)
```

**Step 4: Traversing the Graph with DFS** Create a graph instance and add vertices and edges to it.

Perform DFS on the graph and display the traversal order.

```
if __name__ == "__main__":
g = Graph()
# Add vertices and edges to the graph
g.add_vertex(0)
g.add_vertex(1)
g.add_vertex(2)
g.add_vertex(3)
g.add_edge(0, 1)
g.add_edge(0, 2)
g.add_edge(1, 2)
g.add_edge(2, 0)
g.add_edge(2, 3)
g.add_edge(3, 3)
print("DFS Traversal (Starting from vertex 2):")
visited_nodes = set()
dfs_recursive(g.graph, 2, visited_nodes)
```

**Step 5: Walkthrough of the DFS Execution** Explain the step-by-step execution of DFS on the provided graph.

Highlight the visited nodes and the order in which they were visited.

**Step 6: Conclusion and Recap** Summarize the key points of DFS and its importance in graph traversal.

Recap the steps of the DFS algorithm and the code implementation.