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Select all the graphs that are trees. B.

Select all the graphs that are trees. B.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Educational Content: Identifying Tree Graphs #### Instructions: Select all the graphs that are trees. #### Graph Descriptions: 1. **First Graph:** - **Vertices:** A, B, C, D, E, F, G, H - **Edges:** - Connects A to B and C - Connects C to D and E - Connects E to F - Connects G to D, F, and H - **Explanation:** - This is not a tree because it contains cycles and multiple connections between nodes. 2. **Second Graph:** - **Vertices:** A, B, C, D, E, F, G - **Edges:** - Connects A to B and C - Connects C to D and E - Connects E to G and F - **Explanation:** - This graph is a tree. It is connected and contains no cycles, with precisely the number of edges equal to one less than the number of vertices. 3. **Third Graph:** - **Vertices:** A, B, C, D, E, F, G, H - **Edges:** - Connects A to B - Connects C to D, E, and F - Connects G to E and H - **Explanation:** - This is not a tree since it doesn't form a single connected component with no cycles. #### Key Concepts: - A **tree** is a connected graph with no cycles. - A tree with \( n \) vertices has exactly \( n-1 \) edges. #### Activity: - Analyze each graph and determine whether it qualifies as a tree based on the properties outlined above. Select the graphs that meet the requirements.
Transcribed Image Text:### Educational Content: Identifying Tree Graphs #### Instructions: Select all the graphs that are trees. #### Graph Descriptions: 1. **First Graph:** - **Vertices:** A, B, C, D, E, F, G, H - **Edges:** - Connects A to B and C - Connects C to D and E - Connects E to F - Connects G to D, F, and H - **Explanation:** - This is not a tree because it contains cycles and multiple connections between nodes. 2. **Second Graph:** - **Vertices:** A, B, C, D, E, F, G - **Edges:** - Connects A to B and C - Connects C to D and E - Connects E to G and F - **Explanation:** - This graph is a tree. It is connected and contains no cycles, with precisely the number of edges equal to one less than the number of vertices. 3. **Third Graph:** - **Vertices:** A, B, C, D, E, F, G, H - **Edges:** - Connects A to B - Connects C to D, E, and F - Connects G to E and H - **Explanation:** - This is not a tree since it doesn't form a single connected component with no cycles. #### Key Concepts: - A **tree** is a connected graph with no cycles. - A tree with \( n \) vertices has exactly \( n-1 \) edges. #### Activity: - Analyze each graph and determine whether it qualifies as a tree based on the properties outlined above. Select the graphs that meet the requirements.
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