Questions: (c) give the degree of each vertex. (d) give the number of components of the graph.

Solution Steps

• The vertices in the graph are \( A, B, C, D, X, Y, Z \).
• The edges in the graph are \( (A, X), (A, X) \text{(loop)}, (A, Y), (B, X), (B, Y), (D, Z) \).

• Vertex \( A \): Connected to \( X \) twice (loop counts as 2) and \( Y \). Degree = 3.
• Vertex \( B \): Connected to \( X \) and \( Y \). Degree = 2.
• Vertex \( C \): No connections. Degree = 0.
• Vertex \( D \): Connected to \( Z \). Degree = 1.
• Vertex \( X \): Connected to \( A \) twice (loop counts as 2) and \( B \). Degree = 3.
• Vertex \( Y \): Connected to \( A \) and \( B \). Degree = 2.
• Vertex \( Z \): Connected to \( D \). Degree = 1.

• The graph can be divided into two components:
  1. Component 1: \( \{A, B, X, Y\} \)
  2. Component 2: \( \{D, Z\} \)
  3. Component 3: \( \{C\} \)

Final Answer