**Problem 3: Graph Isomorphism****Objective:**Show that the two drawings represent the same graph by labeling the vertices and edges of the right-hand drawing to correspond to those of the left-hand drawing.**Explanation:**The image presents two different drawings of graphs that may represent the same graph structure, also known as isomorphic graphs. Graph isomorphism involves a one-to-one correspondence between their vertex sets and edge sets that preserves adjacency.**Left-Hand Drawing:**- **Vertices:** The graph includes vertices labeled as A, B, C, D, and E.- **Edges:** Connecting these vertices are the edges labeled f, g, h, i, j, and k. - A is connected to D by edge f. - A is connected to E by edge g. - B is connected to D by edge h. - B is connected to E by edge i. - C is connected to D by edge j. - C is connected to E by edge k.**Right-Hand Drawing:**- **Vertices:** This graph also contains five vertices, though unlabeled, arranged in a different spatial configuration.- **Edges:** The connecting lines (edges) appear similar in number and connectivity rules but are visually laid out differently.**Task:**To demonstrate isomorphism, one needs to label the vertices of the right-hand graph such that they correspond directly to those in the left-hand drawing. This involves finding a mapping for the vertices of the right drawing to the vertices A, B, C, D, E and ensuring the edges correspond to the same connections as those defined in the left-hand graph.**Conclusion:**To solve this problem visually, trace potential paths and test combinations to find a match where each vertex and edge pair align identically between both drawings, demonstrating that they indeed represent the same graph despite their different appearances.

Answered: 3. Show that the two drawings represent…

3. Show that the two drawings represent the same graph by labeling the vertices and edges of the right-hand drawing to correspond to those of the left-hand drawing. f k

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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Question

**Problem 3: Graph Isomorphism**

**Objective:**
Show that the two drawings represent the same graph by labeling the vertices and edges of the right-hand drawing to correspond to those of the left-hand drawing.

**Explanation:**

The image presents two different drawings of graphs that may represent the same graph structure, also known as isomorphic graphs. Graph isomorphism involves a one-to-one correspondence between their vertex sets and edge sets that preserves adjacency.

**Left-Hand Drawing:**
- **Vertices:** The graph includes vertices labeled as A, B, C, D, and E.
- **Edges:** Connecting these vertices are the edges labeled f, g, h, i, j, and k.
- A is connected to D by edge f.
- A is connected to E by edge g.
- B is connected to D by edge h.
- B is connected to E by edge i.
- C is connected to D by edge j.
- C is connected to E by edge k.

**Right-Hand Drawing:**
- **Vertices:** This graph also contains five vertices, though unlabeled, arranged in a different spatial configuration.
- **Edges:** The connecting lines (edges) appear similar in number and connectivity rules but are visually laid out differently.

**Task:**
To demonstrate isomorphism, one needs to label the vertices of the right-hand graph such that they correspond directly to those in the left-hand drawing. This involves finding a mapping for the vertices of the right drawing to the vertices A, B, C, D, E and ensuring the edges correspond to the same connections as those defined in the left-hand graph.

**Conclusion:**
To solve this problem visually, trace potential paths and test combinations to find a match where each vertex and edge pair align identically between both drawings, demonstrating that they indeed represent the same graph despite their different appearances.

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