Consider the graph G : Which of the graphs below is isomorphic to G? OA A Z Z X OC Z T Indicate the isomorphism by listing the vertices separated by commas in the order they correspond to A,B,C,D,E,F,G, respectively.
Consider the graph G : Which of the graphs below is isomorphic to G? OA A Z Z X OC Z T Indicate the isomorphism by listing the vertices separated by commas in the order they correspond to A,B,C,D,E,F,G, respectively.
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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![**Graph Isomorphism Exercise**
Consider the graph \( G \):
[Graph G]
- Vertices: A, B, C, D, E, F, G
- Edges: Connect A-D, A-E, A-F, B-C, B-D, B-G, C-D, C-E, D-E, D-F, D-G, E-F, E-G, F-G
Which of the graphs below is isomorphic to \( G \)?
**Option A (Graph with Vertices H, W, U, T, X, Y, Z):**
- Edges: Connect H-U, H-W, H-X, T-U, T-W, T-Z, U-W, U-X, W-X, W-Y, W-Z, X-Y, X-Z, Y-Z
**Option B (Graph with Vertices V, U, T, W, X, Y, Z):**
- Edges: Connect V-U, V-W, V-X, T-U, T-W, T-Z, U-W, U-Y, W-X, X-Y, X-Z, Y-Z, Z-V
**Option C (Graph with Vertices V, U, T, W, Y, X, Z):**
- Edges: Connect V-T, V-W, V-U, T-W, T-U, T-Y, U-W, U-X, W-Y, X-W, Y-Z, Z-X, Y-X, Z-W
Indicate the isomorphism by listing the vertices separated by commas in the order they correspond to A, B, C, D, E, F, G, respectively.
---
**Explanation of Diagram**:
Each graph involves seven vertices with specific connections representing the edges. The task is to find which graph corresponds structurally to the original graph \( G \), respecting the same connectivity among the nodes, though potentially labeled differently.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0db8c0f3-7e1f-4cf8-bdbd-38ddd8711042%2Fe3d8a276-4c9f-4684-86cd-c831a88f506f%2F7c3w88mp_processed.png&w=3840&q=75)
Transcribed Image Text:**Graph Isomorphism Exercise**
Consider the graph \( G \):
[Graph G]
- Vertices: A, B, C, D, E, F, G
- Edges: Connect A-D, A-E, A-F, B-C, B-D, B-G, C-D, C-E, D-E, D-F, D-G, E-F, E-G, F-G
Which of the graphs below is isomorphic to \( G \)?
**Option A (Graph with Vertices H, W, U, T, X, Y, Z):**
- Edges: Connect H-U, H-W, H-X, T-U, T-W, T-Z, U-W, U-X, W-X, W-Y, W-Z, X-Y, X-Z, Y-Z
**Option B (Graph with Vertices V, U, T, W, X, Y, Z):**
- Edges: Connect V-U, V-W, V-X, T-U, T-W, T-Z, U-W, U-Y, W-X, X-Y, X-Z, Y-Z, Z-V
**Option C (Graph with Vertices V, U, T, W, Y, X, Z):**
- Edges: Connect V-T, V-W, V-U, T-W, T-U, T-Y, U-W, U-X, W-Y, X-W, Y-Z, Z-X, Y-X, Z-W
Indicate the isomorphism by listing the vertices separated by commas in the order they correspond to A, B, C, D, E, F, G, respectively.
---
**Explanation of Diagram**:
Each graph involves seven vertices with specific connections representing the edges. The task is to find which graph corresponds structurally to the original graph \( G \), respecting the same connectivity among the nodes, though potentially labeled differently.
Transcribed Image Text:**Graph Construction Task**
Construct a graph with vertices \( J, K, L, M, N \) whose degrees are 3, 1, 1, 3, 2, respectively.
**Task:**
Determine the edge set of the graph based on the given vertex degrees.
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