Originating at vertex C, how many tree subgraphs and spanning trees are present in this graph?

Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
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Chapter1: Computer Networks And The Internet
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**Graph Analysis for Educational Use**

The graph provided consists of points (vertices) and lines (edges) that connect these points. Here’s a breakdown of the graph and its elements:

### Vertices:
The graph has the following vertices:
- A, B, C, D, E, F, G, H, I, J, K, L

### Edges:
The edges connect the vertices in the following manner:
- A is connected to B, D, F, and J
- B is connected to C
- D is connected to E
- F is connected to G
- J is connected to K
- H is connected to I

**Graph Structure:**
- This graph has multiple branches originating from various vertices. 
- Notably, vertex A appears to be a central point with multiple connections, suggesting it may act as a hub.

**Question:**
"Originating at vertex C, how many tree subgraphs and spanning trees are present in this graph?"

### Explanation for Educational Purposes:
- **Tree Subgraph**: A connected subgraph with no cycles that connects all its vertices.
- **Spanning Tree**: A subgraph that includes all vertices of the original graph and is a single tree.

To approach the problem, consider different paths and connections starting from vertex C and analyze how they branch out to form trees or connect all vertices.
Transcribed Image Text:**Graph Analysis for Educational Use** The graph provided consists of points (vertices) and lines (edges) that connect these points. Here’s a breakdown of the graph and its elements: ### Vertices: The graph has the following vertices: - A, B, C, D, E, F, G, H, I, J, K, L ### Edges: The edges connect the vertices in the following manner: - A is connected to B, D, F, and J - B is connected to C - D is connected to E - F is connected to G - J is connected to K - H is connected to I **Graph Structure:** - This graph has multiple branches originating from various vertices. - Notably, vertex A appears to be a central point with multiple connections, suggesting it may act as a hub. **Question:** "Originating at vertex C, how many tree subgraphs and spanning trees are present in this graph?" ### Explanation for Educational Purposes: - **Tree Subgraph**: A connected subgraph with no cycles that connects all its vertices. - **Spanning Tree**: A subgraph that includes all vertices of the original graph and is a single tree. To approach the problem, consider different paths and connections starting from vertex C and analyze how they branch out to form trees or connect all vertices.
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