(c) Prove that the two graphs below are isomorphic.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Transcribed Image Text:### (c) Prove that the two graphs below are isomorphic.
#### Figure 4 Explanation:
- **Description**: Two undirected graphs, each with 6 vertices.
- **Arrangement and Vertices**:
- **First Graph**:
- Vertices are arranged in two rows and three columns.
- Top row, from left to right: Vertices 1, 2, 3.
- Bottom row, from left to right: Vertices 6, 5, 4.
- Edges connect the following vertex pairs: (1,2), (2,3), (1,5), (2,5), (5,3), (2,4), (3,6), (6,4), (5,4).
- **Second Graph**:
- Vertices labeled a through f.
- Vertices d, a, c (vertically inline).
- Vertices e, f, b (horizontally to the right of vertices d, a, c, respectively).
- Edges connect the following vertex pairs: (a,d), (a,c), (c,e), (e,a), (b,d), (b,a), (f,e), (c,f), (b,f).
### (d) Show that the pair of graphs are not isomorphic by showing that there is a property that is preserved under isomorphism which one graph has and the other does not.
#### Figure 5 Explanation:
- **Description**: Two undirected graphs.
- **First Graph**:
- Pentagonal arrangement with 5 vertices.
- Vertices labeled 1, 2, 3, 4, 5 (top vertex to bottom, clockwise).
- Edges connect: (1,2), (2,3), (3,4), (4,5), (5,1).
- **Second Graph**:
- 4 vertices labeled a, b, c, d.
- Vertices d, c (horizontally inline, d is left of c).
- Vertex a above d and c.
- Vertex b right of a but above other vertices.
- Edges connect: (a,b), (b,c), (a,d), (c,d), (d,b).
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