Determine whether the following graph is a bipartite graph. [ HK If yes, specify the disjoint vertex sets.
Determine whether the following graph is a bipartite graph. [ HK If yes, specify the disjoint vertex sets.
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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Discrete math problem attached.
![**Question 1:**
Determine whether the following graph is a bipartite graph. [Blank space for answer] If yes, specify the disjoint vertex sets. [Blank space for answer]
**Graph Description:**
- The graph consists of 10 vertices labeled from \( v_1 \) to \( v_{10} \).
- Vertices \( v_1 \), \( v_2 \), \( v_3 \), and \( v_4 \) are aligned horizontally and connected sequentially in a straight line as follows:
- \( v_1 \) is connected to \( v_2 \)
- \( v_2 \) is connected to \( v_3 \)
- \( v_3 \) is connected to \( v_4 \)
- Additional vertices are connected vertically or diagonally:
- \( v_5 \) is connected vertically to \( v_2 \)
- \( v_6 \) is connected vertically to \( v_3 \)
- \( v_7 \) is connected vertically to \( v_4 \)
- \( v_8 \) is connected diagonally to \( v_4 \)
- \( v_9 \) is connected diagonally to \( v_6 \)
- \( v_{10} \) is connected vertically to \( v_9 \)
This structure needs to be evaluated to determine if it can be split into two disjoint sets of vertices where no two vertices within the same set are adjacent, which defines a bipartite graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e41cc9b-7a55-46c1-8b1f-6045ac18fd60%2F9bef8473-fc05-4762-a43f-3a08f57c5c49%2Fq54kt78_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 1:**
Determine whether the following graph is a bipartite graph. [Blank space for answer] If yes, specify the disjoint vertex sets. [Blank space for answer]
**Graph Description:**
- The graph consists of 10 vertices labeled from \( v_1 \) to \( v_{10} \).
- Vertices \( v_1 \), \( v_2 \), \( v_3 \), and \( v_4 \) are aligned horizontally and connected sequentially in a straight line as follows:
- \( v_1 \) is connected to \( v_2 \)
- \( v_2 \) is connected to \( v_3 \)
- \( v_3 \) is connected to \( v_4 \)
- Additional vertices are connected vertically or diagonally:
- \( v_5 \) is connected vertically to \( v_2 \)
- \( v_6 \) is connected vertically to \( v_3 \)
- \( v_7 \) is connected vertically to \( v_4 \)
- \( v_8 \) is connected diagonally to \( v_4 \)
- \( v_9 \) is connected diagonally to \( v_6 \)
- \( v_{10} \) is connected vertically to \( v_9 \)
This structure needs to be evaluated to determine if it can be split into two disjoint sets of vertices where no two vertices within the same set are adjacent, which defines a bipartite graph.
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